Hi, I am doing the same research. William M Moore was my g.g.grandfather. His wife was Mary Elizabeth Deborah (not Barret). His father, Micajah Moore married Rutha Cabaniss. After Micajah died (about 1822), she married a Joseph Barret. That's where that name comes from.
My Line is: Micajah->William Micajah->William E->John James (Jackson)->John James (Jack) - Me.
The great mystery is Micajah's history. Supposedly, he is the son of Nitakechi, but I can find nothing to verify that. Also, supposedly, his mother was Salina Moore, but again, I can find no independent verification of her existence..
It's been several years since you wrote that, so I hope you're still active. Any information I ahve is yours, and I hope you can fill in come gaps for me.