Saijo , Giombo and Suruga are the best three by far of about 20 kaki persimmons I have tasted. Hachiya is also among the best.
I know Jerry Lehman had a huge collection of native persimmons in Indiana and was working on commercializing frozen pulp. I met him several times over the years at fruit growers meetings and tasted some of his breeding selections over 20 years ago. Some had very little astringency and good size. A few of his native persimmons were just as good or better than the kakis and I think he had some hybrids. Was sad to hear he passed away last year. If you do a search with his name and persimmons you will find links to people that he shared his plant material with.
BTW, the furthest South I have have seen native persimmon trees was near Daytona off the Southbound I95 shoulder and also in the Gainesville area off 301. Those trees might be good to use in Florida for rootstock. Persimmons are my grafting nemesis, only one take out of at least 50 tries when I lived in South Carolina.
I suspect black sapote might possibly cross with Kaki or American persimmons or be graft compatible to grow Kakis easier in low chill areas of Florida. Good black sapote cultivars have taste similar to a pollen variant kaki but fruit and seeds are much larger. Black sapote are really a persimmon species too. Australia seems to have the best cultivars of those. My Dad has a mature Black sapote tree, maybe I will attempt grafts or save a few seeds for those that would like to try. I think black sapote would do well in San Diego.
I did about 20 bud grafts here in SC and only got 2 to take.
I am always on the lookout for Persimmon Cuttings! So far I got Prok and Tam Kam to take.
I will be trying again this year. There are about 10 American Persimmon trees in my yard that came with the house and some are about 30 feet tall and have fruit.