I only have them in small groves so I can't say I have ever even considered thinning them. I will also say that the native ones I have don't seem to do as well in full sunlight. They grow fine in full sun, but only seem to produce fruit well in the broken sunlight. They are an understory tree and seem to thrive best in that role from what I have seen. I am not sure "thinning" them will have the result I think you are after (more fruit). I would maybe try it and see what happens before you go crazy with a saw. I also don't see any deer interest in them. Coons and opossums seem love them...
I have a lot of them as well...but they don't all produce the same. The ones that produce for me are more mature trees in bottom land/flood plain areas where there is decent soil moisture, but it drains well. The areas also tend to have a decent overhead canopy as well....maybe 50% sun. These tend to be the cooler areas in the woods in the summer heat as well and I am not sure if that has anything to do with it or not. This is what I have seen with the native trees here....I am sure their are different cultivars that are different and I see some folks plant them in an orchard type setting. I tend to start seeing fruit in late summer here (roughly early/mid Aug). I get some that will fill the palm of your hand...but most range in size from that big to the size of a walnut or so.I got tons of these but can't get them to make fruit.
For deer - my opinion is that pawpaw are a waste of time and effort. Others may not see it that way, but I just don't see the deer use of them. Now also keep in mind that if you have paw-paw growing, that you may need to reduce the canopy even higher to get the light you may need/want. No point in removing the paw-paw just for other "junk" to grow. I know in the areas I have paw-paw if I cut them down the first thing I would have grow would be buckeye, sycamore, hackberry, walnut, ironwood and other "non-deer value junk". Also keep in mind that paw-paw are a colony type plant so I would suspect that they would try to re-grow to at least some extent.Sorry for the misunderstanding, by thinning I was referring to getting rid of them so other things could thrive
I like a little diversity as well, but if the woods was over-run with them, then I can certainly see removing some to try to get some other diversity.I'd keep paw paw around just for the diversity and interesting growth of them. Even though mine don't produce fruit, they sure look cool---especially in the fall. Like I've said numerous times, when I'm not seeing deer, I sure like to look at pretty woods. Aesthetics put my mind at ease.