You are right Prunus serotina grows in your area. Actually, I have seen many trees here in Highlands County. I think this is the southern end of its natural range, though. However, I believe that has more to do with soil than chill because I have seen some trees fruit with less than 50hrs of chill here. There was a nice fruiting tree in the neighbor's yard, but it was cut down when new people moved in. Fortunately, a seedling sprung up in the fence row but it has not fruited yet. At one point, the University of Florida made hybrids with the closely related Capulin, but I don't know what became of them. Apparently the Capulin didn't thrive in Florida.
While Okame does not produce fruit, the Taiwan Cherry (Prunus campanulata) does, and is apparently very popular for its pink blooms in your area. People rairly see the fruit, though, because birds like it so much. It is more closely related to sweet cherries than Black Cherry and I read once that it makes good jam. I have not been able to find that link again, though. It might be worth looking in to.