Have you found him on enough census reports to be able to say which county he lived in for sure? Back then, there was no standardized spelling of anything and people just spelled it anyway they could. My friend has a will on her ggg grandfather and his last name is spelled three different ways in ONE will!! There is one more place you can try. Have you tried writing to the Bassett Historical Center in Bassett, Virgina? They have more material than what they advertise and a lot on people in Franklin County as well as records. You can even call with your request and they put request in order they came in and bill you like 10 cents per page of what they find, and they kind of do like a small donation! They have helped me with Franklin County people on more than one occasion. Give them all the information you have and they research it and mail it to you. Other than that, have you tried contacting the Franklin County Historical Society? The ladies there do research for $20 per hour, I think. One of them may be able to come up with a family group sheet, or family genealogy or a death cert or a burial for you. I have used them too, but if you go to Virginia, you can go the the FCHS and do your own research free and they will help you.
If you have more information on your Woody, you are welcome to write me with it and I will try to help you , but with what you have, it is so little that he is hard to find.
Have you tried tracing documents backwards in time for his direct descendants? Maybe something along the line will give you a clue. Try marriage licenses, wills, birth and death records. You can get free death certs on reels from the library of Virginia if your local library has an intra library exchange program. Just ask your local library.
Meanwhile, if you can tell me anything more, I will be glad to try to help you. Here are some links:http://www.bassetthistoricalcenter.com/
and my email is: firstname.lastname@example.org://www.franklincountyvirginiahistoricalsoc.org/