What's the process of getting retro-active permits on work like this?

That way you know they are active in the BP community!

I bet the city would squeeze it in this year to get some $.

Ya, just from a quick pull in AirDNA, the Conway market has 1700 active STRs so that's promising.

If they have money and can compete on pricing, brokers will be the best bet.  

A vacation rental could generate higher returns but requires more active management.

You do that, it's going to be best place to start because I am betting from there you will seek how to simplify things. 

Unlike some buyers, I ALWAYS go look at the properties before the sale and discovered that the vacant lot had an active railroad track on it and therefore was unbuildable, and would remain unbuildable until the railroad removed their track. 

I would also look at like kind properties that are listed and active in that area too.

And yes, they ARE actively policing it.