I cast my vote for the South Holston. That river has a lot of potential.
I'm not sure about the Obey. I think most of the trout records from the Obey came from before the 1970s. Keep in mind that the Cordell Hull impoundment wasn't closed off until 1973. Before Cordell Hull stopped the water and let it warm up, the Cumberland was cold enough to support trout as far downriver as Carthage. I even have a sporting magazine where they were stocking the new Cordell Hull reservoir with trout and Atlantic salmon in the late 1960s, though when they closed the dam off completely, apparently the water got too warm and that was over for good. Anyway, I suspect that most of those record trout in the Obey in the 1950s and 1960s were big bruisers that migrated in from the Cumberland.
Incidentally, one other "sleeper" source of record browns might be Dale Hollow Lake. They haven't been stocking browns in Dale for long, and nobody knows how big they could get. They have some potential, and very little fishing pressure. I think the guy who posts here as Fishfindergeneral is the only person I know who is even fishing them consistently, and I believe he's already picking up a few in the 8 to 10 pound range.
bd