John, I have worked on Parham / Stith geneolagy for many years, mostly Parham. I have talked to many who have done the same. The best I can come up with is that Richard is either the brother of William or the son of William, brother of Stith Parham who married Elizabeth Parham. I do this by adjusting the time line of when Richard and Elizabeth may have married and then trying to project when Richard was born. This is a very flawed way of doing things. For one, is this Richards first marrage? I have the Rev. War records for Richard, what is left of almost nothing.
Off the top of my head, as I do not know how to put my hands on them right now, the woman who was claiming a pension on the service of Richard was from North Carolina. She was claiming on the grounds of her son being the son of Richard. Her name was not Elizabeth if I remember right. At this time I do not remember what her name was, but I do remember trying to find her, her son, her new husband. I found absolutly nothing. I looked for months and decided that the records pertaining to this matter were distroyed in the wars and fires that ravadged the area. I have been to the supposed grave of Richard outside of Milledgevile GA. I have researched the grave sight and have decided the grave is a phony. I talked to the man who owned the land at that time (1995) about the obvious earth work that had been done to make a small dam for stock to drink out of. I talked to an elderly survayor who was also a geneolagist. He had survayed the area many times over the 60 yrs. he worked. I have come to the conclusion that the headstone marks no grave. I believe it is a ruse for someone a long time ago who wanted to gain acceptance to the DAR.
All this is speculation based on a LOT of research.
If you come across any info which sheds new light on this suject I would like to see it . I will be glad to share any info I have.