I would increase the amount of great content and improve the quality of the content that is already in place.  Content is what people link to.  Great content = quality links = high DA.

If the rankings of the criminal defense pages have direct links then those links are helpful to any query that any page of the site competes for.  So, I would not delete them.

There are law firms with strong websites that rule the SERPs for everything in their town.   Their office takes any call that comes in, accepts the cases in practice areas where they have interest and expertise, and refers the rest to other firms for a referral fee.

The specific page has.....  >500 domains linking to it.

This is rocket fuel.   Irrelevant articles help lots of websites.

Find the person who wrote that article for you and give them a really nice gift.

Ask them to write another article about plants in the office.

Ask them to come up with some great photos of plants (that you are legally able to distribute as screensavers, branded lightly with your domain) and give them to people.

Advertise the new article about plants on the popular page, advertise the screen saver on your popular page.

I don't think that you are going to kill a software giant with irrelevant articles but I believe from experience that they can be very helpful to your rankings.   Plus, we make a few sales every month to people who landed on our website to consume irrelevant content - and the products that we sell are irrelevant to the content and damn few people want what is sold on that site.

So, how big of a mega menu are we talking about?

Ten links?  Fifty?  A hundred?

I think if you go waaaaaayyy to big it can be a problem with both usability and SEO.  But the SEO problem is not in the link dilution.

Wow!   Tom, that was a very generous and expert response.

Nice work!

I'd slap some big Adsense on it and enjoy!  

I believe that one off topic page will not hurt anything - especially if the page is an outstanding example of content for its topic.

I know sites that publish on a wide range of content and have fantastic rankings.  These sites were once single topic,  then departed with a single page that struck gold - and then started plowing that field into a hundred pages,  and soon ranking #1 for the single-word root keyword.    They then hit gold on a second topic, and a third.  Now these sites have diverse branches but have found ways to interrelate the topics.

I don't think that Google has a problem with conflation.  You might even make Google think that the two topics are complementary.

This problem has been around for over 20 years and thousands of companies who have used shortcuts lost a domain to penalties and algorithms.  They call this the doorway page problem, the jump page problem, the cookie cutter page problem, the portal page problem, and a dozen other names.

If you want all of these pages you will need to put a team of people onto the task of writing substantive content for each city.  If this company is truly large enough to deserve thousands of doorway pages then they should have the resources to author substantive and unique content for each one.

In the question between a subfolder and a subdomain...  it is clear and it is murky...

Search engines say things and often do the things that they say.  They also do things without sayin' that they did them and you are left to figure out what happened or how things work on your own.

If you have been running websites for a long time (24 years here), you might know that Google and other search engines have treated subdomains and folders differently,  identically and murkily.   It depends upon what year and month you are talking about.

**The constant is that subfolders have always inherited ranking ability from their parent domain, and will likely do that into the future.  **

So, if you want assurance into the future, using a subfolder is your best bet.

Looking at DA... it is irrelevant in the subdomain and subfolder discussion.  DA is a moz number that kinda correlates with search engine rankings, but just part of the time.   Ranking ability and DA are different things.

Go to archive.org to see your old title tags.

Your SERP CTR can drop when Google changes the SERP interface.  They can slap more images, ads, videos, "people also ask" , news and various types of rubbish that absorb the clicks before your organic rankings are seen.    Competitors above or below you could start adding kickass prices, free shipping, or free beer to their title tags.

.... but, my usual suspicion is that the developers monkeyed with something.

"I've had someone tell me that google doesn't pay attention to H3 tags -- only H1 and H2. "

Pay this person no mind in the future.

The answer given by Nicholas White is perfect.

We don't compete in your space, but we do have a site that competes by keyword overlap with sites that advise on alternative medicine.  The overlap consists of at least 100 keywords, many of which have a monthly volume of 10,000+

The comparisons of our site vs alt med sites are as follows...

university degrees and government-issued licenses   vs.   author panache and social cred

scientific terminology  vs.  common language (which has a higher search volume)

factual information  vs.  lore and creative writing

Over the past two years, on three occasions, we have received substantial improvements in rankings and traffic as the alt med sites have dropped.  I attribute it to Google wanting  the SERPs to be populated more with formal credentials and technical prose rather than with lore and panache.   We intentionally improved how our E-A-T is displayed about two years ago and I think that has been helpful.

In these situations, a person can only guess at what might be doing this, however, other sites similar to ours have seen the same improvements at the same times.

Imagine the population of people who are interested in the bedroom topics that you have written about...  I think that they would fall into three groups...

1. people that enjoy the "dirty talk"

2. people who don't care about it - they just want to read the content

3. people who are put off by the "dirty talk" and don't share the content or even read it very far

I think that group 1 would continue reading if the language was cleaned up, but if the language was cleaned up group 3 might appreciate the content and read it and value it.   Google might have a similar view and discriminate against "dirty talk", unless the searcher has safe search turned off.  So cleaning the content up might improve rankings.

You said... "this one continues to tank".   What exactly does that mean?  A slow and steady ranking and traffic decline?  A slow and steady loss of traffic through external links?    Or have there been a small number of sudden drops in visitors, in rankings, in revenue?

If your answer is "slow and steady" then I would bet that much of the loss is coming from the increased competitiveness of the internet and the emergence of new competitors.   Anyone who owns a 15 year old site that has not been getting a lot of regular new content and existing content improvement is seeing this.

If the losses are small and sudden, then it could be algo changes at Google that is knocking the site because they don't approve of something.   Just speculations.

I think that it is extremely risky.  The more work and money that you have invested in the website that will be the recipient of the redirect the greater the risk.

This is a methond for people who do not have a big investment in their website and are simply looking for a low effort way to gain a small amount of ephemeral juice.

PDFs can be canonicalized using .htaccess.  Google is usually very slow to discover and obey this but it can be done.  However, if your PDF is not close to being an exact copy of the target page, Google will probably not honor the canonicalization and they will index the PDF and the html page separately.

https://www.inmotionhosting.com/support/website/how-to-canonicalize-images-and-pdfs-with-the-htaccess-file

PDFs can be optimized (given a title tag) by editing the properties of the document.  Most PDF - making software has the ability to do this.

You can insert "buy buttons" and advertising in PDFs.  Just make an image, paste it into the document and link it to your shopping cart or to your target document.

PDFs accumulate linkjuice and pass it to other documents.

Use the same strategies with PDFs as you would with an html page for directing visitors where you want them to go and getting them to do what you want them to do.

Some people will link to your PDF, others will grab your PDF and place it on their website (in that situation, you lose the canonical but still get juice from any embeded links), and benefit from ads and buttons that might be included.  Lock the PFD with your PDF-creating software to prevent people from editing your PDF (but they can always copy/paste to get around it).

Other types of documents such as Excel spreadsheets, PowerPoint documents, Google images, etc can have embedded text, embedded links and other features that are close to equivalent to an html document.