@Nick Hulme smart idea to start investing out of state! A few things here: why is the "best strategy long distance long term rental properties"? It could be, it depends on a lot of factors: risk tolerance, goals, timeline, expertise, etc. You don't dig in to those for you personally here, I'll assume you looked into those and determined that this was the best strategy for you personally. (There are a lot of possible strategies, and they all are the 'best' for the right person!)
BRRR can be great, if you're going to do that, read David Greene's book on long distance real estate investing, and do what he says in terms of working with contractors. It is certainly challenging to oversee any rehab, after all you're getting more reward by taking on more risk. If you actually do what David Greene recommends, you greatly increase your chances of success.
In terms of markets, most on your list are ones I'd consider already pretty played out, expensive, with non-optimal rent/return ratios. I think you want the NEXT Nashville, Austin, etc., you don't want to be buying into those now. In fact, for both of those, I work with several investors who even live in those markets, and are investing here in Chattanooga instead.
I think you're right to focus in the southeast, I'd just move to smaller cities where there's still more opportunity!