Kathleen, glad to see your post and an update on where the persimmon program is currently.
There are a few threads I’d recommend reading through if you haven’t yet, and there is a lot of information and a bit of unnecessary side banter in some of the tangents. Importantly, you’ll find information about your questions on PCNA chances, polygamodioecious parents (thanks @Lucky_P for reminding me about that term), and astringency loss.
Short answer I can think of for seedless fruit would be selecting both northern and southern trees and having future growers go with whichever is not present in their location, assuming cold hardiness is not an issue. As you will find, there are a few of us working on cold hardy PCNA breeding projects.
The most important thing with persimmons, as I’ve come to learn about farming and fruit growing in general, is that you don’t know what you don’t know. I’m confident in the hundreds of hours I’ve spent learning about them that I’ve only scratched the surface and there are many people on this forum (and the various nut growers associations) who know more than I ever will and that much knowledge will be lost as the older generations pass. The recent interest in this fruit in the past couple years on this forum has led to some very worthwhile discussion and I would hate for you to reinvent the wheel on topics already covered. I wish you luck and please continue to update us and ask for help!