You poor kid, you!Yes, it is hard to find records on people of color back then. I have never worked with slave records before, but have you specifically checked for them wherever you go? Edward may have been a slave at one time OR he may have been a freed man, one never knows! Wm.Draper also.
I am curious how Edward Woody had a son named William Draper! Unless of course, he was a slave and sold to a master named Draper.That is all I could figure out.
How about starting by working backwards with a death cert on William Draper and see what it says. The Bassett Center does have some pre 1912 death information, but if he lived to 1912, to at least age 66 , Virginia did start recording them at that time and there may be one! You seem to know when William died, what year was it? Richmond does charge $12 for one and will do a ten year search for it both ways, forward and backward in time 5 years to find it. If that does not work, then you can try finding Wm.Drapers' kids and their obits to see what those and any death records on them you can get say. I mention this because if you hire a professional, they are at least $50 per hour! That is one chunk of change. You yourself can order a lot of certificates for $50 bucks an hour!
Let me ask you what makes you think Edward had any connection to Franklin County? Can you tell me what the connection is? I see your dilemma and my heart goes out to you. I will try to help you as much as I can. I like the research and volunteer to do this in my county and state. I used to volunteer for RAGOk and now for 3 sites in my state. Why don't you send me your email address and full name? I don't think I even know your name! I will keep it and send anything I find directly to you.That way we don't have to keep corresponding here. Don't know if I will be successful, but am willing to try. Here is my email address:firstname.lastname@example.org