If not Persimmon, I say magnolia virginiana. Never seen a paw paw. Only read about them in Donald C. Peattie's book. Very familiar with persimmon and sweet bay.
It would have been the first magnolia I guessed. But It seemed too obvious. They're common around here. Not really eye catchers. If I posted one I would expect a pretty quick Id from one of you. But as I check the natural range I notice that RI is too far north. Not a common tree for you.
Actually, I'm wrong. They're not 'that' common. I see them once in a while in natural settings and as ornamentals . But X's tree looks like one. But I still think that's too obvious a guess. It's gotta be something else. They grow wild in RI?