FSN - sounds great. :-D
Buckeye - they sure do. I'm told that Delaware is the heaviest hunted public land in Ohio. Who knows if that's true, but it seems to be popping every time I've been up there. Alum Creek is quite a bit smaller but there are always hunters (and horse riders, and hikers, and fishermen, and boaters) there when I go.
I really doubt you will find much public land in this area that doesn't get hammered but that's the way it is.
The one bit of public land I found that seemed relatively lightly used (somewhat close) is the Ohio Power land out by Zanesville. I hunted that a bit several years ago and much of it seems pretty decent, it's just farther than I really want to drive in the morning. You do (or did when I hunted) need to get a free permit to hunt that land, but getting permission is no big deal.