To throw another wrench into the mix: you could also ride the east side of the Blue Ridge. Others here seem to have good info for the Valley; all I can say is 340 doesn't sound fun but I know there are goo roads out there. Usually either up against the Blue Ridge (parallel to 340) or over the next hill into the Alleghenies.

But back to my original comment: on the east side of the Blue Ridge, you follow 810, a lovely road, all the way to 33. From there, you have the option of crossing back over to the valley, or going to Madison and 231. I've never ridden 231 so I can't comment on its suitability for cycling. Finish off with 522, which is four lane but with a decent shoulder, I think.

I can provide more details if needed.

When are you going to do this?