That picture of the trunk with no leaves made my stomach turn. I have the same issue with my two peach trees, they grew huge. Two years ago I had 5 yards of mushroom compost dumped on the spot between the two trees, when one tree was about three foot tall and the other hadn't been planted yet. Maybe that had some affect. The Elberta is blocking light from the Asian pear and attacking the elderberries. I once had a nice path between the peaches, blackberries, and elderberries, which is gone.
So, just to be clear, I can prune it now, in late summer, and everything will be okay? This goes against everything I have known about pruning, but I trust the experts in this forum more than anything else I have read.