I've been to Fruit & Spice Park many times. The Redlands variety (tree is unmarked) is right is next to the asphalt path, near the "SES2" variety, also near path, which produces small fruit (have not tasted).
I've eaten a few of the Redlands, and it is sweet and mild with a hint citrus. Maybe a tad bitter near the peel, but not offputting.
Off the path a bit but still near the Redlands is the Smathers variety (marked) which makes large, bumpy fruit (did not taste).
The Smathers sounds more like what you described (softball sized), since I have not noticed Redlands variety to be as big as softball sized.
Another part of the park has the Bonita Springs variety. To me, they taste the same as the Redlands. I've read that Bonita Springs is self-fertile.
Julie:
Membership is definitely worth it. I think White Sapote season at the park start around May and goes into June-July.