Florida is part of the Southern Tier, so you won't be avoiding Florida if you ride the ST. That said riding the ST across Florida is almost all very rural with widely spaced towns and millions of acres being used to farm pulp wood. It would be easy enough to stealth camp most if not all of the time with no need for rolling in late.

I recommend that you go in a Feb-Mar timeframe if doing the ST. That is when I rode the ST and it seemed the best time to find cool temperatures with longer daylight hours than late fall and early winter. I had one bitter cold night on a pass, frost quite a few nights and temperatures that reached at least the 50s every day. I did see a little snow on the roadside a couple times on passes, but none on the road. If the passes do get enough snow to be an issue it usually melts in a few days. Having a little extra time in the schedule for that is probably prudent.

I wouldn't worry much about the gators, but be careful of the fire ants and plan for protection from mosquitoes. Also there are venomous snakes, but you probably won't see any and I wouldn't worry much about them.