Now I am getting a little excited!! My Elijah's gravestone says 1860, so it's possible that your 1861 Elijah is the same.
And my Elijah had a brother named Green, and so does yours. I also noticed that your Elijah had a brother named Dial. My Elijah named one of his sons Cledis Dial Williams.
Maybe this is it!!!! I am being very cautious, because once I tracked down an Elijah Williams who was definitely the WRONG one, and I was so disappointed. So--let me clarify--the list of children you sent me were the children of John T. Williams and Frances (Frankey) Ritchie? Thank you.