Here are some directions provided by Jonathan at the PDC:
I took this route to Ashville in April. The route was great until we got up in the mountains and hit rain and fog. Not being able to see anything sort of defeated the purpose of driving in the mountains.
This route gives you a little time on the Blue Ridge Parkway. However, don't take the BRP north of Ashville because it's closed (or at least was closed in April).