I live just north of Chattanooga and have driven the route described. The route has one section about 15 miles from Cleveland TN beside the Ocoee river that is very crooked. It has a couple of very sharp turns, but no switch backs and no shoulder. This section is about 6 to 8 miles long, but has little elevation change in this section. Other than the 6 to 8 mile section, the road is easily navigable with a motorhome. This route is also 4 lane much of the way. If you are willing to navigate a few miles of tight 2 lane, this route is beautiful.
The easier route, and almost as scenic is to take I-75 north from Chattanooga to I-40 east to Asheville. This route should be a little quicker. One word of caution.
You mention highway 129. Be very careful that you do not get on the portion of 129 that crosses from Tennessee into North Carolina. Go to WWW.tailofthedragon.com and look at the map, you will see what I mean.