Im a fan of 308 win and 30-30. If i lived in NE Tennessee i would probably just use a 30-30 and be happy. Before Covid ammo for it was very cheap.
But i dont live in the same location as the OP and live on the Idaho/Montana border. Despite my 30-30 and 308win appreciation i got into my Ruger compact 338RCM rifle a few years back and its my favorite hunting rifle. Part od my affection for the 338RCM has to do with the cartridge and the other half is the rifle it comes in. The rifle has a short action and 20" barrel with iron sights. Its compact enough and light enough but not abusive in recoil. It knocks elk hard but then again i had no issue before with the 308win and took some bigg critters with the measley 30 cal back in the day. Still i like the upgrade in performance with my short and fatter 338.
