This turned out to be more of a challenge than route 28.
There's no other option for parts of the route between Culpeper and Charlottesville, so I just went for it.
Parts of the way, there's a half-decent shoulder (though it's only about half the size of the big one on Pulaski Highway between Philly and Baltimore). Sometimes it gets really narrow--strong encouragement to pedal like crazy until you get through the narrow spot.
My safety strategy was to watch my mirror carefully, and when two cars are next to each other (no room to get over), make sure there's a lot of shoulder room, or else stop and get off the road. I only had to get off the road a couple of times.