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Sorry for the cliche response, but I would worry more the quality content than the length of the content.  Are your users going to feel fulfilled with less than 300 words?  Maybe for some topics.  I doubt there is a magic number to get links.

If you are churning out blog posts of an "optimal" length but they aren't engaging you probably will not see any benefit.

Long story short: Don't worry about the length.  If you are writing just to write, you probably shouldn't expect much in return.

I've found this as a good source in the past, not sure if you have already checked it out:

http://www.internetmarketingninjas.com/blog/search-engine-optimization/301-redirects/

It is true that you will most likely not be penalized for these pages, Google is pretty good at figuring out common canonicalization problems in my opinion and would most likely not penalize you for having duplicate content.  I would encourage you to dig a little deeper and see what additional problems these pages could create though.

Consider that Google will waste valuable crawl bandwidth crawling these meaningless pages, rather than focusing on the important content you want them too.  If Google is crawling them, you can most likely bet that PageRank is flowing through these pages as well, diluting the link equity of your site.

Are you using Wordpress?  There are a lot of great plug ins that can help you manage these pages.  You could control how Google crawls these pages with your robots.txt, by placing meta robots tags on the pages using a plug in, or by placing rel=canonical tags on the pages pointing back to the page that is the original source.

I guess it all depends on the relative importance of the keywords and landing pages.  If the pages that were hit are important landing pages that drive conversions it should be something that is addressed.  If the pages are being penalized, on-page optimization probably won't help too much; however, building quality back links could have some benefit.

It's possible that rankings have decreased on certain pages because the links that were helping the pages rank are no longer valued, rather than the pages receiving direct ranking penalties.  If this is the case than building some quality links to replace the ones that are no longer valued may help the pages rank well again.

What worries me the most is when you say the company is going to switch to "white hat only for a few months" (not exactly sure how you meant it, so forgive me if I read into it wrong).  Things are never going to improve if white hat tactics are only a temporary strategy.  Google is only going to get better at picking up shady tactics.

I would look into installing a module called Global Redirect.  It should take care of this problem for you.  I used to work exclusively in Drupal and made sure this was installed on every site.

https://drupal.org/project/globalredirect

http://developerkarma.com/2008/04/22/step-step-guide-installing-drupal-module-global-redirect.html

I misunderstood you before, I thought you meant the old URLs had the anchors.

You are correct, technically the tabs are not unique pages.  You would have to redirect each of the previous pages to http://www.teapigs.co.uk/tea/matcha_shop rather than to the anchored URL.

Having content under tabs may limit your ability to rank for a variety of keywords.  For example, if previously there was a page ranking for "What is Matcha?", it may now be difficult to rank for this term because there is no longer a unique page dedicated to the topic.  You lose the ability to have a unique URL, Title Tag, Meta Description, H1, and so on.

Are you seeing these 404s in Webmaster Tools or when crawling the site?

If WMT where does it say the 404 is linked to from? Click on the URL with the 404 error in WMT and select the "Linked from" tab.

Crawl the site with Screaming Frog and your user agent set to Googlebot.  See if the same 404 errors are being picked up and if so, you can click on them and select the "In Links" tab to see what page the 404 is being picked up on.

I checked the source code of some of the pages on www.kempruge.com and didn't see any relative links which usually create problems like this.  My bet is on a site scraping your site and creating 404 errors when they link back to your site.

I crawled your site and didn't see the 404 errors.

I did notice that your sitemap in your robots.txt 404's so you may want to take a look at that.

If the main category is Digital Marketing then I would have the URL be /digital-marketing/.  I think its important to consider how you plan to use the category in the future and build for that so you don't have a funky structure in the future and/or have to do a bunch redirects to fix it.  I understand that's not always possible and things may come up you hadn't considered.