There are available in stores now, fuyu persimmons, the flat
ones. They can be eaten out of hand, but they're hard. I
bought 10 of them at Costco Monday morning.

If you freeze them overnight and then let them fully thaw,
they'll be very soft. Scrape the flesh out of the skin and
either use it as is, or add a bit of sugar and whisk it.
Like blueberries, whisking persimmon flesh/juice will cause
it to thicken and set solid upon being chilled.

That will work well instead of a jam.

Pastorio