One way to find out is to make a small batch. Jelly that hasn't been through the whole jar-sterilizing circus will keep for a week or so in the refrigerator, long enough for you to figure out if you like it.

Looking at the texture of the fruit, I'd use an apple butter recipe as the guide for the basic process but not use the apple butter spices.

i've never heard of the sapodilla, but if it's like the cheramoya and the sour sop (as that link is leading me to believe), then you can freeze the flesh. soursop makes amazing shakes! i would look up recipes for preserving its cousins and use those as a roadmap.

I don't know what the pectin content is like on these, so if you make jam with them you may need to add some pectin or apple juice to get the texture right. You could also try preserving them in a honey syrup if you don't want to go to the jam route.

Send them my way to california, I LOVE them :)

They are common in India and you can make milkshakes using them