I don't think we've connected before, but I have to say there are many Skelton's in the area that can't be traced to each other. If you haven't already, you might need to refer to the book "John Skelton of Georgia" where Jabez and Richmond show up in an extensive genealogy.
If you went to Hartwell, you might have seen Richmond's name on a history sign in the courthouse yard talking about what he did. But you won't find the name of my 3rd great grandfather, Noel Skelton, who built the first county courthouse. And you might find that he's not related to Richmond, at least not in any way we can trace. He was reinterred at Mt. Hebron Baptist Church when they built Lake Hartwell.
My ancestors are also buried in the Sardis Baptist Church graveyard, and I thought I had pictures of all the markers there, but I don't have one like you describe. I had also looked over the minutes of the church meetings from 1854 which list some Skelton names. It made for some interesting reading!
Anyway, even though we may be looking at different branches of Skeltons, maybe we could share some information.