Hi William,
First off, I have never done something similar personally, but until someone either contradicts or confirms my thoughts, I will give you my opinion from a theoretical point of view.
I would do as you suggested first - create subfolders for the specific locations onto one national site. Then I would redirect the local domain pages to the specific page on the national site, if this wasn't too much work. If it is too much work, I would just 301 the whole of the local domain to the subfolder that roughly correlates. This would just redirect any link from the old local domain to one new location.
Having subfolders on one national domain means that you will have all of these incoming links from the local websites (and the value from any backlinks). Every one of the subfolders (assuming your architecture is good) will benefit in some way from all of the backlinks. Win-win. Your site should flurrish with this approach.
With regards to having separate local sites with a link back to the national site, this will only pass on a fraction of the link juice value, and most would be retained by that local domain. I've always likened having lots of local websites to kind of hedging your bets. Hoping for local search value.
I think with good architecture and a good backlink profile, you can easy rank better, even for local searches, with a national website.
I welcome other people's opinions though!
Best,
Matt