I don't think that John and Anestes are the parents of Eliza at this point. I think they are of our Oakley Clan. I find that Hannah in her application for Cherokee claims, said Eliza's parents where Williams and Anetes (it is hard to read here but it looks like Anetes last names is Lynch or French or something with a nch on the end.)
I have become suspicious of Hannah. She claims Anetes was full blooded. Hannah also at this time is applying for CSA soldier widow pension.