Unit L over in the western half of the state used to allow 4 does a day, period. A couple of yrs ago they changed that to 4 does a day if you had a permit of some kind. I think a nuisance permit or something like that. The rules change as TWRA decides on population in given areas.
I've left the house with the potential to get into trouble at least once thinking it was a doe weekend, and it was in Unit B but not in Unit A, and living in the Oak Ridge area it is very easy to hunt both depending on which way you turn out of the driveway, Roane is in a different unit than Anderson. When I had my house in Oak Ridge I lived about 500 yards into Roane.
I know how you felt, lol. I grew up in Oak Ridge, so when I left after graduating from high school, I quickly discovered that not every gun club had a thousand yard range like ORSA did, and that actually, almost none did. My only advice to the OP is to keep looking and ask around whenever you encounter other shooters, as there are often good opportunities in East TN that are also not widely advertised.
The "Varmint" of choice when I was kid was wild boar, a different game from Chuck's, but as much fun in its own way.









