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Heard through some of their customers that the links they built got sites hit with manual penalties last year. I wouldn't personally use them for this ... just depends on the business & goals, I suppose.
Keep all your reports if you do use them. Check the links, verify you aren't getting setup with sites that can harm you.
You should test your actual page out with Flang
If it shows as working in there, it's just WMT being slow. If it's not right in there hopefully you can see why from the message.
Oh how right you are. There was nothing like the feeling of fighting my way into spot #20 and then someone came "online" (either active again or staffer) and I was suddenly 21 ... #no #notNOW
Trivia: I think you and I are the only two people in the top 20 of both Inbound & Moz. You have the lowest combined "number" of anyone at 3 + 17 = 20. I am 20 + 13 = 33. Rand would be tied with you (15+5, I think) if he were on the Moz board.
Thanks for doing this & that's pretty awesome data. I think it's cool to see who the helpful members are and what they're doing to be helpful. It's interesting how the data has changed over time as well. Some of the long-term Moz users have more posts written & more blog comments but fewer Q&A. The top people from the past 12 months are practically the opposite with way more Q&A involvement (people like Patrick, etc.)
This is more philosophical than technical but the more control over something you have, the more chances there are for things to go wrong that you have to fix as well.
So really, this comes down to control vs. problems. If you want full control, Wordpress is the way to go. It's more flexible and will do "anything" SEO needs you to do. Weebly will have some limitations but comes with far fewer problems.
Where that scale balances out is definitely up to you. I use Wordpress because I prefer control. My sister uses something like Weebly because she doesn't know "what a PHP is."
My questions were just the tip of what could be wrong. As I said and Moosa repeated, you are likely going to have to hire someone as a consultant to solve this. There are way too many factors at play on why you may have lost some organic lately. Competitor improvements, your own site not crawling properly, parameters & duplicate content confusing Google, new site structure loads slower, etc.
There aren't another 3-5 questions we can ask to sort this unfortunately. Someone needs to dig in with your site, analytics, etc. to see what's going on. Exact dates matter (algorithm updates) as do how everything is setup for your redirects and all that. As I said, Archive.org saw your redirect as a 302. That could hurt you. There could just be so many reasons.
Private network - essentially if you own all those sites that are linking to you, all using the same template, etc. that's potentially very bad. Especially when done the way you've done it.
If you're using an SEO agency who is building links from sites like hottubgalaxy (dotcom) for you, they're doing a very poor job of hiding their intent. If you are doing this yourself, stop it.
You obviously know a little about SEO given your exact anchor text link to start your question ... but even that, here on Moz, is kind of suspect in most cases. You could just give us the URL.
Bing and Yahoo rely more on on-page content for new sites than they do backlinks. Google prefers a good solid base of people linking to you most of the time.
According to Ahrefs you have 53 backlinks from 21 domains. 3 of these domains (and 12 links) are from Edmonton home & garden shows (ie. all the same people). Only 13 of these links are dofollow links and 40 are nofollow - a very strong ratio against you.
You also have pages that don't land in the same place they used to. You have links to /poker-tables/ but that redirects to /game-rooms/#poker-tables
Your Ahrefs anchor text shows about 48% of your referring domains link to the site using the word "hot" and 33% "tubs"
The backlinks you do have from sites like Hot Tub Galaxy, Hot Tubs for All, Just Cat Fishing, etc. are all extremely suspect and look like blatant spam to me.
I would suggest that the better question to ask would be: "why would Google rank this site at all?" At the moment, nothing off-site suggest they should. Sorry for the bad news. (Btw. if that's your PN, that's not how you do a PN.)
I can think of a few ways...
Did "organic" include traffic from another search engine that is now entirely gone? I ranked #1 for "domains" on Bing for a day or two. Guess what that did to my traffic? lol
Analytics may not be setup on all new pages. Traffic going to (for instance) blog posts that are posted to social and then picked up by Google but not yet crawled? I had a REALLY big client who had installed GA once but never followed up on all their (manually created) pages. This is why I love Wordpress and template CMS but hate everything else. You can run a Screaming Frog crawl that checks whether the GA code is on every page.
Was the GA code used on ANOTHER site and subsequently removed? WMT would only show you the one site. The same GA code can be posted to 10 sites. When 8 go down, your organic traffic would decrease but your WMT would stay the same.
I'm sure there are at least another 5 ways that this could happen. It would definitely require a bit more investigation but yes, both can happen at the same time.
You are likely going to have to hire someone as a consultant to solve this. There are a lot of factors at play:
Was the traffic you lost 40% of all organic? Or overall?
What was your main source of traffic on the .net site?
Did you run Adwords in the past and stopped them?
Do you have a manual penalty from some of the spammiest links in your link profile?
Page-by-page comparison of the old & new sites: site speed, on-page contents, all the technical coding, etc.
Things like domain age, 301s not passing 100% of benefit, etc. will be affecting you but there could be other factors. It's very difficult to diagnose such a problem like this. Your old site had been online since 2008. That's a good amount of site age.
Also, back in September, Archive.org (Wayback Machine) found that your redirect was actually setup as a 302.
When I do a manual crawl myself or header check I see that it's setup as 301 but whatever sent them a 302 may have also been passed onto Google. I would want to check the WMT/Search Console for your site, Analytics and then maybe you'd be a lot closer to having an answer.
Hope that helps some.
I have a couple of great Upwork consultants who freelance with me who you'd have to pry from my cold, dead fingers. I love Upwork and I use it to find new talent. Yes, you do have to sift through some bad but it's worth it. When you find the right people to complete your team it's like magic!
Freelancing, I believe, is the way things will mostly all move in the future. I am happy to jump in now and get ahead of those who don't embrace that future.
I don't believe there's a way from the user side to cancel a crawl. However, your competitor won't get notified of anything. Moz doesn't have their email address or phone number to contact them. 
The tool crawls their site like Google, Yahoo, Ahrefsbot, Majesticbot, and all the other web search engines do. They will not even notice that you ran this accidentally. It's similar to doing a crawl of a site with any other search engine or tool.
It will literally never come to this but if they question it, blame your SEO guy. Everyone else does. lol Say "my SEO guy must be doing some competitor research." Us SEO guys do that all the time for pretty much every client. We'd not really be doing our job if we didn't.
301 redirects do not pass 100% of the link "juice" you have earned for the original page. There's a longer discussion about it here: https://moz.com/community/q/how-much-juice-do-you-lose-in-a-301-redirect
Most SEOs I know say it generally passes about 90% of the value. But what I've found is that it passes more as each link is rediscovered by Google as well. So if you had an eBay homepage link and it's scraped every 10 minutes, you'd get the juice from that link back much quicker than a blog post from 2011 that Google may never visit again.
I would say just keep working on the site & move forward. You'll either always be around 90% of the previous juice so keep working or you'll gain most of it back over time as those links are re-checked, so ... keep working.
Yeah, Google used to scrape Yelp but was under investigation by the FTC for doing so. I don't think they still do though some of the older data (like 2011, 2012) may still be there. I can't imagine they're still doing it.
Wow, you have a LOT of spam in your backlinks. Have you done a disavow or had a penalty with this site?
I think Peter adequately answered your question - PageRank isn't an accurate measure of anything - but keep in mind that DA & PA can be manipulated as well ... with a backlink profile like yours you will probably see a higher DA than you "deserve" because DA doesn't really take spam into account nearly as much as Google does.
The most important thing I'll be doing in 2016 (and I think probably the most important for nearly everyone) is consistency. I kick a lot of tail in bursts. A burst may be a couple hours, a week or a quarter ... but I'm rarely amazing for a full year. lol I want to add a lot of consistency to my blogging, my work and all my interactions.
As long as you're working in the live/work, I don't see the problem with doing this. Why do you think it may not be correct?
Sent you a PM with an option (not something I do but I know a company who may be useful.)
If it's related to your industry and most of your competitor sites have the same type of links, that may be what Google expects to see. I think site speed & backlinks are two places where every niche is unique to itself.
In a site speed example, I've seen photography keywords where every page 1 result the site takes over 8 seconds to load. Now, in an informational, mostly-text niche like say "george bush biography" that would be really, really bad. I think Google would expect to see sites in that niche load very fast. But photographers all have these full screen images, large portfolios, they're showing off the work, etc. I think the algo rightly realizes that if MOST sites that return a keyword are slower than average, site speed probably counts for a bit less overall as the distinctions are smaller.
Same with backlinks - if your competitors all have these borderline links and they have authority, and you remove yours, I would fully expect your site to drop rather than rise in the rankings. Disavow is good for removing authority but doesn't often give you a positive bonus. It just keeps you from negative problems. To beat a competitor you don't need to avoid the negative. You need to add positive. I would focus on that side of the equation to see the best results.