fruit trees that are not "pome" or stone fruit

That’s so interesting. Seriously. Has anyone eaten it? I want some.
And, pawpaws have a weird smell when fruit is on.
OP, maybe crabapple trees would work. They are so pretty in the spring.

My cousin had fig trees in Chicago. They were hard planted and very productive.

And yes, American persimmons are the ones you would need.

Also grapes,blackberries, blueberries and kiwi berries.

And much to my surprise, even cacti.

Grapes grow on trees? You learn something every day.

It’s the other way around - grenades are named after pomegranates.

Most Breadfruit varieties have to be cooked (baked is best IMHO). Its quite starchy and tastes something like a sweet potato, not like any sort of sweet fruit. And like a potato,you get filled up fast so you can only eat a little. They are quite large, somewhere between a soft ball and a basketball. Even though they grow all over Hawaii, you’d be hard pressed to find them on a menu even in a local restaurant. Local “Tutu’s” know how the prepare them; try to get invited to someone’s home for a meal. They are almost always in season. The trees produce year round and the fruit holds on the tree for a long time.

I have Muscadines. They are most definitely on a vine. They will climb up a tree if allowed to. You have to prune with a vengeance to keep them in line, on the vine, as it were.