I think you had the right idea, but the wrong route. Perhaps if you cut the corner by going from Elkhorn City, KY to Christianburg, VA, you would cut about two days off by following the route. Go to Google Maps and drag the "Yellow Man" over so you can see what roads are paved. There are a lot of smaller state highways and county roads (not 460) which you can take. By using streetview, you can spot check the road to see if you like it.
You could do the same from Christianburg to Richmond. A quick glance makes VA-24 to Rustburg, VA (heck of a name for a town) a bit promising. Again, just look for roads you like. You can try the "bike route" mode but be sure to check the route via Streetview and/or satellite view as it likes to route onto busy roads then onto gravel roads. Just spot check the route, make adjustments, and keep pedaling.
Best wishes on a successful (and quick) ending.