It looks like you've decided to take the direct route. Your way will be shorter, but you'll have a few challenges to deal with:
- It looks like you're following US 421 and 25E a fair bit, which will have more traffic than the TransAm route.
- 25E has a "no bicycles" tunnel up near Cumberland Gap.
- You'll get to see a lot of east Tennessee ridges. There's so few N-S roads over those sections of ridges, you might be surprised how heavy the traffic will be.
- The bridge over the Holston River south of Bean Station has fairly wide lanes, but only two of them.
- IIRC, the section of 25E over Bulls Gap is two and three lanes without shoulders, and it is the most direct route between Morristown and Greeneville.
- I don't remember Lower Paint Spring Road, hope it's paved. The best way to drive a car from Greeneville to Hot Spring was to take 321 down to Parrotsville and then over to Del Rio.
Why would I suggest a longer route?
- Adventure Cycling does a pretty good job of picking out good roads for bicycling.
- Taking the BRP only leaves you with about 30-40 miles of roads where bicyclists are uncommon.
- As I noted, I-26 has taken a lot of traffic off 19 and associated roads. And the route from Damascus down to Elizabethton has a good road, lightly trafficked until you get close to Elizabethton.
It's a "horses for courses" kind of thing. What do YOU look for in a bicycle touring route?