Call your district forester.....ask him to come look at the woods....tell him what you want to accomplish and listen to his advice. These guys know trees and wooded landscapes and how to shift the ecosystems. IT could be the best thing you ever did before thinking about dropping old trees!
dogghr, sweetgum, hickory, elm and a few other secondary hardwood species are opportunists in low elevation high rainfall humid areas (probably maple etc at your elevation).....when preferred dominant oak hardwood is removed for whatever reason these secondary non-preferred species are in the position to shift dominance quickly in their favor. The easiest way to degrade any plant community is selective removal or selective overuse of preferred dominant species. If a clear cut is truly a clear cut then each tree species is cut to the ground and each regrowth has access to the same resources and all compete uniformly (or some regrowth is controlled)...gradually shifting over centuries toward true oak balance/dominance. However, there always seems to be this kind hearted mankind approach which wants to 'leave something behind standing'...the obvious thing to leave behind or not destroy is the secondary species due to low economic value.....and in several decades that is exactly what you have....a forest of low value secondary hardwood! I don't know if you remember the drive just over the mountain from the house and I pointed out some woods to you which had been cleared in the 80s by dozers and chains....and I mean leveled excepting 3 trees per 80 ac....then left to succeed! Here we are know 35 years later and it is a postoak dominant upland woodlot now in need of thinning or fire. We also didn't look at the bottom by the gate where I selective cut for post oak firewood in the same time frame leaving shumard oak seedlings behind (the shumard wood smelled like dog shit and no-one wanted it). Shumard are now mast bearing and in need of cull thinning to restore the understory vegetation diversity. I did not know what the hell I was doing back then other than cutting wood for income....but it seems to have worked out in a very positive way in terms of species diversity and complexity and a fit of the right successional tree species to the right ecosystem.