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We have informational and retail websites where we put a LOT of effort into our content.   We are trying to produce the best-on-the-web.   All of this content is created and edited by people who have both formal education and deep experience in the content area.

There is no way that we would allow user-generated content on these websites - even though we are not in a YMYL (your money, your life) type of industry.   User-generated content can be excellent, but a high percentage of it is deeply flawed and far, far below our editorial standards.   We have experience people in our own industry who want to submit content but we reject it because it is below our quality standards.

The above is why we don't allow user-generated content based upon editorial standards.

I have read information published by Google where they say that a vigorous comment section can be a sign of a quality website.  But, I believe that applies to content types where opinion, kibitzing  and prattle are acceptable.  However, medical sites (and other types of websites) are an entirely different matter.   Low quality content can result in problems for the reader - even if it is in a comments section.  Nobody knows exactly how Google views this, but I am going to protect my visitors from BS and poor-quality information.

Magdalena's example shows that you understand the problem.   Implementation might significantly improve your situation.  And just as important... implementation will enable your visitors to see Magdalena's credentials.   Do it for your visitors even if Google is not a concern.  Your authors also deserve to have this work done.

I absolutely agree that "the quality of the copy is more important than the number of times that the keyword is used."   I don't believe that I have ever calculated my keyword density because I believe that the quality of the copy is (almost) EVERYTHING.   Some people will scoff at this, but I know for a fact that if the quality of the copy is high enough that linkbuilding is not necessary... it enables you to spend all of your time on the copy.

You should write in natural language.  That might produce a very different keyword density - especially if the article is really long.  Google can tell when you are stuffing in the keywords.  Readers think that you don't know how to write.

If a person considers his business and the industry where he will compete, the keywords that are most profitable or most precious are usually obvious.   Having identified them, the work is then to build one very high quality page for each of those keywords and then forming that page into a finely-crafted arrow with characteristics that will defeat all opponents.

When in difficult contests, multiple subpages are then built, each to attack a subkeyword and these are prepared so that they might provide deep content resources, backlinks to the page attacking the root, and demonstrating to Google and all visitors that yours is the world's best resource.

The attack might be short but if the prize is worthy, years might be required.  And, for this deep knowledge and strong writing skills will be required of you, and possibly assistance from allies.

The tracking most valuable for all of the above is the ranking position of your root and primary subkeywords.  As time progresses you will hopefully see increases in the rankings as you put your work forth.  Those ranking increases will be the fuel that  keeps you moving forward and keeps your mental energies high.   Nothing is more valuable than mental energy when in this type of competition.

The difference between a 301 and a canonical...

With a 301, you set it up and it immediately moves the visitor and the link juice to a new URL.  Guaranteed - as long as you hold the 301 in place (mine will be up until I am a dead man - and beyond if instructions in my business continuity plan are obeyed).

With a canonical, the visitor is not moved to the target URL, thus lost traffic.  You also must trust google to obey the canonical (and they often do not, especially if the old and the target URL have differing content.

Comments....

"Developer says old site can go away, but people searching for it are still prevalent in search."   If this was my business, the developer would be ordered to set up the 301s.

"We attempted to use 301 redirects to redirect to the new url and prevent the draining of link juice. In the end, according to the developer, it just isn't going to be possible without losing all the existing link juice."    I am not an expert on this... but I do know that when "developer says that it just isn't going to be possible" often means... "I don't know how to do it"... "I don't wanna think hard to figure it out"...   and that a better developer can often get the job done.   If this was my business, I would be looking for a highly skilled developer to help the current developer with this problem.   The current developer might learn something, or I might look like a dumb biz owner to him.  I'll take the risk with my ego but I will not risk my biz to avoid taking a risk with the developer's ego.    It's all about ego and I risk mine all of the time to get things done using best practice.

You will place the same canonical tag on both pages...

The page at www.domainintheserps.com/product-a/ will appear in the SERPs.

The page at www.othersite.com/product-a/ will not appear in the SERPs (if google finds and obeys your canonical tag)

The value of all links (including internal links) that point to www.othersite.com/product-a/ will be transferred to www.domainintheserps.com/product-a/       All of those links will show in your Google search console backlinks.

If your pages are not identical or if Google doesn't like one of your sites or one of your pages, it is possible that Google will ignore you instructions.  Canonical tags are suggestions not commands.   Also, Google can be very slow to find and obey canonical tags.  It can take months.

Your page at www.othersite.com/product-a/ will sometimes appear in the SERPs for any of the following queries

site:othersite.com

site:domainintheserps.com

site:othersite.com product-a

site:domainintheserps.com product-a

So, your competitors can figure out if you are doing this stuff.

I forgot to answer one of your questions... "Does it still index"?       Maybe.  It will likely be indexed upon discovery.  Then, at a later time, the canonical will be obeyed and it will drop from the SERPs.

Google recognizes synonyms and will often give you ranking credit for them.  We have a site that shares lots of photographs.  We call them  "photographs" on the site, but Google ranks our pages in the SERPs for many other keywords that do not appear on our site:  These include:   images, pics, pictures, photos, and more.  Google often bolds those keywords from the query in the SERPs - as if they appear on our page.

You received a great reply from Alex.

We have lots of problems with content theft and go after much of it.  Our response depends on WHO has grabbed the content and republished it.  If our content is used on a dirtbag spammer site we go straight to the DMCA form that  Alex linked to.  Google responds to them, often the same day, and almost always within three or four days.  They remove the infringing content from Google search. We have done this hundreds of times.   (If you have many to file, you can use the back button of the DMCA form, edit what is different and send it in again).

If the content is on a large blogging site like WordPress or on a large forum, Google often tells us to go there and have the page taken down.  These sites usually respond promptly.

Before you go cranking out  DMCA at scale, if is a good idea to consult with a copyright attorney to learn about fair use or similar concepts in your country.  There are many ways that someone can use your content without breaking copyright law.  If you have someone taken down where fair use applies or where your claim to copyright can not be documented, they you could be on the receiving end of civil legal action.

Sometimes, more frequently than you think, we find our content on sites that should damn well know better than take our content.  These have included law firms of all sizes,  police departments, district attorneys, government regulatory agencies, government law enforcement, or simply the website of an honest and respectable company.  In these cases we don't go to DMCA.  These folks need education. So our attorney gets in touch with firm but friendly greetings.   The culprit is often someone at their office who works on the website and took some shortcuts in content development.  Also, their SEO or web developer grabbed our content, added it to the website and charged them for the content.   These cases of content theft piss you off, but watching what happens can be entertaining.

ADDED:  I forgot to address your main question.  Can content theft and republication hurt your rankings?   YES IT CAN.  Some of the sites who steal content are powerful and can outrank you.  In addition, you can lose long-tail traffic because your words on their page combine with other words on their page and outrank you in the long tail.

If a lot of websites steal the same piece of content, Google can have trouble deciding who owns it - even if you have a reasonably powerful site and the content has been on your website for a decade.  Google says that they are "good" at identifying the owner, but I don't agree.  We had important pieces of content descend into supplemental search results after a lot of other sites had stolen it.  It only emerged after we spent a lot of energy on DMCAs and direct legal notices.

.... each of your pages/articles would still be focussing on a single keyword (or keyword cluster) while bearing in mind the overall goals.

You are 100% correct.  They are all about the same long tail keyword with even longer long tail keywords as variants.

You wouldn't have two pages competing for "Stihl Chainsaw MS170 Maintenance" for example, but you might have multiple pages that are talking about "Stihl Chainsaw MS170" in various ways, all probably linking to the page where the customer could buy the actual product or parts, etc.

You are right.  And, those pages linking to one another will support the attack on "Stihl Chainsaw MS170"... and all of them plus all of the pages for other models will support the attack on "Stihl Chainsaws".

1. You should avoid having multiple pages focus on the same keyword because you will lose some control of which result will show.

First, disclosure.   Most people will consider me to be a heretic when it comes to keyword cannibalization.   I embrace it, I advocate it, I practice it, I attack it.... and it makes me a lot of money.

Let's say that I want to sell Stihl chainsaws.  I would write multiple articles about each one.   I would write an article about the features of each model, an article about maintenance for each model, article about the replacement parts for each model (and how to replace them), an article that show the advantages of each model.  There would also be a lot of articles that compare the various models.   We are talking about dozens total, a few articles for each model, and many articles about how to select, ideas for use, accessories, chains, sharpening etc.   When I was done with these articles my site would be the go-to place for these products and would be 10x better than what the manufacturer has prepared.  When you search for one of these saws, you would find two, three or four of my pages at the top of the SERPs.

Lose control over what  content will show???   HELL YEAH!!!  Because all of my content is gonna show up in the SERPs.   People will see that dominance and know that I am The Man for these products and that my site is the go-to-place for the.  All of those pages at the top of the SERPs will push the competitors down and people will come to my site instead of my competitors site.

This is not cannibalization.  This is deep expertise, deep helpfulness, and deep moneymaking.   It's a deep investment of money and time too.   And you really gotta be The Man to be able to produce this kind of site.

2. You should identify your core keywords and weave these keywords multiple times (naturally) throughout your site.

Stop thinking about this.  Just stop it.   Instead, write naturally, paying no regard to how keywords are woven into your website.  You will waste less time chasing the myths of SEO and more time writing great content.

While I am dissing "best practices"....

If you build the chainsaw website described above....  you will not have to go begging for links.  The links will come to you.

The problem with that, is very few people have the knowledge and the willingness to actually buy all of those saws and use them for enough hours to know them.   This experience is what separates the people who really have the content knowledge from those who are faking it.

Why are these links not being clicked?  Are they on low quality websites that nobody reads?  Or are they about topics that nobody is searching for?  Or is the content so low that people quit reading.

Each of these has a solution.  Target better websites, write what people really care about, increase the level of quality.

Now, if you are going to put all of that effort into it, then perhaps the website that you should be targeting is your own.  Filling it full of high quality articles on topics that people really care about and are searching for.

Common wisdom in the SEO community is to spend time building trivial content in the form of guest posts that will produce links that nobody clicks on.   I don't get it.  I'd rather spend my time building a real website that I can be proud of.  Bet on yourself.

The "Radios by Industry" column has so many links in it that it extends off the bottom of the page and is at least 50% unseeable and unusable in both Chrome and Firefox.

'nuff said.

The canonical tag is meant to tell Google....   "These two pages are the same"

It was not meant to prioritize pages in the rankings.

Because your pages are very different from one another Google is probably ignoring the canonical tag.

"should we just appreciate the fact that Google ranks us twice on the first page for this important keyword? "

Yes.  You got two pages in the top ten of Google.  When that happens to me, I give thanks.

The true answer to reinstating the old site depends upon the quality of work done on the many parts of the job by the PR agency.   If this was my site, and it was performing kickass before these PR guys got their hands on it, I would toss the old version back up and do a deeper assessment - because the results thus far suggest that the PR agency doesn't know much about SEO.

<kibitz>In the past few years a lot of PR agencies have become spammers who wear suits to work.</kibitz>

Just saying what appears to work well here...

At the top of each article, immediately under the title, give author attribution such as:

Author:  Dr. Jonathan Egol, D.M.D., MAGD.

The author's name and credentials, if any, are displayed, and the name of the author hyperlinked to a biographical page about the author on the same website.  The hyperlink is coded as  <a rel="author" href="https://etc....

The biographical page contains a few sentences that hit the most important credentials and experience of the author, in a professional tone rather than braggadocio.  (this paragraph is meant for search engines, but also visitors who want to know about the author - this is visitor friendly language and information)  That is followed by details of the author's education, work experience, publications, awards, etc. -- this is listed much the same as what you place on a resume or curriculum vitae.

The biographical page might contain hyperlinks to other pages on the web that give important credentials about the author.  These pages are where third parties have essentially vouched for the author.  These might be:  A) a profile article about the author in a medical journal; B) a google scholar page for the author; C) an article in a professional publication about the author's receipt of an award; D) a page about the author in wikipedia; E) links to government registration pages to prove official licenses; F) links to organization websites that show the author as a trustee, board member, etc. G) profile pages for the author on other websites that list his publications there.

If the person does not have these third-party vouchings, a paragraph explaining years of experience, relevant education, relevant licenses/certifications, areas of expertise, etc.

All of this is followed by a bibliography of the author's most important or most popular articles, with hyperlinks to where they can be found on the web.

Some people believe that the most reliable way to determine keyword difficulty is to visit the SERPs and see who holds top positions and then you will know "who you must defeat".

If you want something a bit more reliable, then click into the top-ranking pages, examine them and then know "what you must defeat".

The combination of who and what is very informative.

Who and what have informed in advance of battles for thousands of years over all types of terrain.

I don't use keyword difficulty scores.  I want the information above.  Then, I match that against my skills and the resources required to become competitive.

Great mistakes are made when skillful people allow keyword scores to scare them away from competition and when low keyword scores lure less skillful people into battles above their abilities.

I'm trying to work out what to do if this is a spammy technique and also affecting our trust scores etc and what we should do about it.

I think that it is a very spammy technique.

First items of work.

1. submit disavows to Google

2. remove this trash from its servers

3. find out who did this.  If a current staff member, I would consider their current worth to the company.  If it is low I would be discharging them.  If it is high, then I would educate them.  If a SEO service provider did this I would cancel any current contracts and not do business with them again.

I have had an account at SEMrush for a long time and they have a long history of what I track.

Place them in menu headings that are relevant and useful for the visitors.

You don't want to have customers thinking... Why did they put this crap in here.   As soon as they start seeing "contamination" in your menu their shopping in that category will end.

What do you think of the Amazon SERPs where they are showing crap in their SERPs that does not match or even relate to the querry?  It has a really bad odor to me.