Algonkian to Riverbend is a float to consider. The shuttle is kind of long, and the first stretch is flat water. You'll have to push through it to Seneca Breaks. At low water, Seneca Breaks could be tricky to get a drift boat through. I would recommend the raft. That said, I’ve found the fishing to be good, particularly on the Virginia side.
P.S. If President Trump, or other "high ranking officials" are playing golf up there, they will shut down access to the river.