I plant in N.E. Ga. so I can not definitively speak for central Fl. I plant my last crop of better boys in mid June. They do wonderfully in the Georgia Hot and muggy August. The only problems I have ever seen have been from people who prune the better boy and the lack of foilage can let some of the fruits get sun scorched.

I'm pretty new to gardening, esp. in Florida, but I "think" if you run into a problem with blossom drop it'll probably be due to nightly lows remaining in the 70F's. Hopefully your Better Boys do better than my Brandywines did last Summer. If they mature and set blooms by June I "think" they should do okay. Sorry, I'm just learning myself. :)

Somebody at the store awhile back said they had Cherokee Purple all last Summer so, among other varieties, I'm trying one of those.

I live on the edge of California's central valley. We have several weeks of 100+ degree heat and up to 110. I havegrown Better Boys for the last three years and they do well if they get plenty of water. My problem is that they tend to split toward the end of the growing season. I suspect that this is due to uneven watering. I now have installed a drip system. I do think though that in this extreme heat they would need a sell established root system to survive. Also I think they would require gradual increasing exposure to the sun. The heat can be relentless. The heat here is
very dry. I was only in Fl. once, but nearly croaked on the humidity. :-)