Every once in a while you see a ride promoted but as mentioned is rare. Ex Cup cars run Time Only (TO) as they aren't legal in any SCTA class ( and really can't be made so) but for your first wish would fit the bill. They still have to meet all the safety rules which can be a chore particularly if, for instance, cage diameter and thickness rules are not met ( a common issue taking ex racers from another sanctioning body) I have no knowledge about what a cup or similar car rules are in that respect. Taking one to build to run yourself not so much for the above reasons. Keslowskis have frequented Wilmington when we ran there and maybe now at the Arkansas site with ECTA though I don't know that for a fact.
Texas mile, Loring and Arkansas are closer, though not close to So. FL. Some rules/classes are different that might make your thoughts closer to reality.
As usual, plan is be safe, have fun. Good luck.
I have friend/crew member in Ocala, similar Drag (Funny car) and road race including SVRA experience and LSR also 2 club member. Has car he has been dragging feet finishing to go back ( I drove for him in the past).. He'd probably be happy to chat with you. He wants to put much bigger motor in it than what I drove and I have suggested he might be on his own with that (though I have been faster than it should go.) Anyway, if you are interested, PM me and I will ask him if he would talk to you.