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I recommend Joseph's approach. There are many benefits to this approach: manageability, scalability, and seo. You can address all the practice areas available in specific locations as well as rank the firm more strongly in each location by key of relevance.
Hi Liana,
As far as spammy links, Google has done well detecting whether or not they are intentional, aka black hat. If they aren't, Google does not penalize you for these links, so it's best to leave them.
As far as a strategy for generating links to your website, you should always focus on high quality over quantity. High quality links give you exponentially more return than high quantity of bad links.
I recommend this article Google wrote for us to understand when and how to disavow links.
https://support.google.com/webmasters/answer/2648487?hl=en
In short, rarely do you ever need to disavow links, even if they have a high spam score. You are only hurt when they sense you are gaming the system and in the case that they detect or suspect unethical backlinking, you will be penalized with a "manual action". You can check if you were penalized, as well as disavow flagged backlinks, in the Google Search Console.
Google has an easy-to-read article for you about when and how to disavow links.
https://support.google.com/webmasters/answer/2648487?hl=en
In short, rarely do you ever need to disavow links, even if they're spammy. They have smart analysis built-in to detect whether a spammy link is just spam or if it is the result of unethical SEO practices trying to game the system, otherwise known as "black hat SEO". In the case that they detect or suspect unethical backlinking, you will be hit with a "manual action". You can check for these, as well as disavow links, in the Google Search Console.
Hello Mike,
This may be hurting your presence on one or the other site. Duplicate content is typically frowned upon. You can get around this by simply assigning a canonical URL in the head of the HTML. A canonical URL tag tells the search engine "hey, the content is also accessible here but the official page is actually at example.com".
I went ahead and checked the HTML of both pages and they already have a canonical URL set to the main website address you posted. So it looks like you're good to go!
No, thankfully you don't encounter the issue of cannibalization between pages. Google or other search engines may use the more targeted page if it's determined to be more relevant , however if it's not determined to be more relevant you will get the page that's already ranked. It won't pull your other page down, however if you are just duplicating the content from the main page, the search engine may choose to skip indexing the new pages overall.
Overall, this should help and not hurt.
No problem Liana.
But yeah that's the gist of it! Instead taking the time investigating and disavowing links, you could spend that time cultivating relationships with other websites and businesses that could give you nice quality linkage.
Hope this answer works for you. 
Your best strategy in beating a spammy website is following the best practices of SEO and web development.
You've already outlined two key components you will need to use: high quality backlinks and rich relevant content. As you've pointed out, generating a wide network of backlinks takes a lot of time and many relationships. That is a big reason as to why links have a high value in SEO. Although it is not as effective as it previously was due to the increasing number of variables, it still holds a lot of equity amongst the signals used by Google. Your .edu strategy should be noteworthy, as only established institutions are afforded this domain space.
Because at first you will be outmatched on the off-page SEO like backlinks, focus on the on-page factors. This includes content relevance, content quality, page speed, and others. You will find a lot of resources available here on Moz that you can refer to.
https://moz.com/learn/seo/on-site-seo
https://moz.com/learn/seo/on-page-factors
Yeah, I don't disagree with you. Algorithmic filtering and ranking doesn't work exactly as intended, and there are ways to work around it as you point out. Generally, cannibalization shouldn't occur, but it does happen in some circumstances.
I should also clarify, these may hurt you if they are your only links. If you have very little equitable links, this may cause Google and other search engines to falsely recognize you as spam. So just be careful and be on the look out for extra suspicious spam links. The balanced approach is the best approach: don't worry but stay aware!
Here is a more technical write-up from Moz that I reccomend: https://moz.com/help/link-explorer/link-building/spam-score
Personally, I would use the one domain. And from what you've said, you would prefer it as well.
Thankfully, rankings are on a domain basis and not an IP basis, so there would be no issue in the first scenario. If you are duplicating and synchronizing the servers, you are better off using the one domain because you aren't creating two separate websites with differing content (UK English vs US English).
Do you have the bandwidth or ability to produce separate versions (for each domain) for each area you want to target? If not you are best off generalizing your website to target all English users instead of en-US, en-GB, etc. You're going to have to evaluate your geotargeting goals and budget.