Pawpaws usually do better, especially in warmer climates, if they are lightly/partially shaded (the whole tree) for their first couple of years. But, if I understood you correctly, your trees are already over a year old and doing OK. If this is the case, and we're already near the end of summer, I'm not sure that adding shade at this point is going to accomplish anything. Maybe if they have been shaded by surrounding vegetation and you are planning on clearing that out...but otherwise, I see no reason to suddenly change what's working in your case.

Christie, the wild pawpaws here taste nasty to me when compared to the better named varieties, so maybe you will like a grafted one better than the wild one.
In mid June, I found about a hundred pawpaw seeds in the fridge, and set them in 2 large pots, very close together. Just about all seem to have sprouted, they are in a sunny location, get at least half a day sun. Next Spring I will divide them and put the better ones in pots and maybe graft some. I have a friend who does this and his get full sun. I have read that shade is needed for the first 2 years, but I have never paid attention to this, and if there is a problem with lots of sun on young pawpaws, I am not aware of it, and neither is my friend. His seedlings grow at a very fast rate.
Benny

I've definitely had better luck with partially shaded pawpaw seedlings than I have with unshaded ones. The unshaded ones often cook for me at the same time as similar but partially shaded individuals did well. So from personal experience as well as numerous studies/reports/texts, I'd say shading can definitely benefit young pawpaw seedlings.

The reason I'm not overly excited about Christie's trees getting shaded is because they seem to have gotten over most of the hump already without it (if I'm understanding her correctly). It would be interesting to know more detail about Christie's situation. Are her seedlings getting a little shade from surrounding brush? Are they getting lots of moisture? Etc...

Thanks - I cut plastic tree protectors to put on them and the seedlings were so small that the protectors covered up everything except for the very top. They get some midday sun, perhaps about four hours. I'm not sure when they start getting shade in the afternoon but I tried to plant them where there would be shade from trees on the west. We had a hotter than normal summer but got pretty good rains except for awhile in August when I should have watered them but didn't get around to it. I was happy to see that they were still alive. The tree protectors that I put on them were missing. There isn't much of a trunk to hold them in place so I suspect that they were just blown away by wind some time during the summer.