Help me Unity!
I know more about NC, but for starters, Roadfood
has some recommendations for the I-81/I-40 corridor. The easternmost spot on their TN map is Ridgewood Barbecue in Bluff City TN, a spot Jody and I would go out of our way (and have) to revisit. It's a little east of Bristol, not much of a detour. I don't have any experience with the others they recommend, but the Roadfood recommendations are pretty reliable. Click on the map symbols and then the highlighted urls and read the reviews.
Their KY map
is a little more sparse, and again, I don't have personal experience down there. A time-honored method, when it's getting on toward meal time, is to ask somebody who looks right (I don't want to profile here, but you know what I mean) where he goes when he wants good barbecue.
(Any time, James.