What about MS?
I would look at Hillside, Mathews Brake, Morgan Brake, and Panther Swamp NWRs. Approx. 40,000 acres, a December rut, and during the archery hunt there will be at most 6-10 deer hunters on the entire 40,000 acres. Plus, the delta is much more of a cultural experience than middle TN. The one downside would be they can't shoot does, but they'll have an opportunity at some of the heaviest bucks in all of America.
They could fly into Yazoo City or Greenwood and find a decent hotel for $30 a night.