I am experimenting with cherimoya varieties in my hot SW Florida climate, its even hotter than Pine Island as Im over 20 miles inland and get higher highs most everyday in summer expecially during the heatwaves.
I grafted some varieties on different roostocks to evaluate but all of them seem to drop leaves and stall growth these last few months. plants are young and sample sizes are small but DR white looks the best so far.
Regarding cherimoya or annonas in general offseason fruit. I first recall when i visited the late Wayne Clifton at his home he was showing off his Dream cherimoya tree. It was febuary 27th and he was selling me scions from his Dream tree. He pointed out the branches he stripped the leaves prematurely on to induce off season flower and fruit. He had fruits fairly large on his Dream annona at this time and flagged the branches with flagging tape to keep track. When the climate is mild the annonas especially the hardier didnt defoliate so stripping the leaves is important to get them to flower as they flower on new growth.
here are photos of Wayne Cliftons Dream annona tree from my visit back in in Feb 2017