To answer your question about travel time via an 'easy pace': The highest posted speed limit along the BRP is 45 mph. The grades aren't prolonged, but it is a hilly drive in many areas. Then of course you have to add in the stops, which considering the scenic drive, may be many. Depending on where you get on/off the parkway, those access roads can be more curvy and inclined making for slower speeds in a RV. I'll add my stops two-cents worth:
Natural Bridge - there's a nice campground there too
Mount Mitchell - highest point. Taking the RV up there is a challenge
Mill Mountain Star- in Roanoke. The two campgrounds aren't anything to brag about
Peaks of Otter - near Bedford
In Waynesville, one of the better campgrounds is Pride. I'd also recommend a trip up the mountain in Maggie Valley to The Swag, but not in your RV. If you're interested in horse back riding in the mountains, there is a stable half way up the mountain at Hemphill.
If you have a sweet tooth absolutely don't miss Whitman's Resturant and Bakery in Waynesville.
I like this website for detailed map of the park way.http://www.blueridgeparkway.org/maps.htm
Enjoy your trip. Wish I were going in Sep/Oct. It will be gorgeous.