I'm interested in your Fannie Oles Buckner -- Did she ever say who she was named for? Every name seems to have a purpose in this line, which is why Onacata is such a mystery. I have a Frances (Fannie) as well, born in 1884, the daughter of Jane (Jennie) Baldwin Johnson who was a sibling of your Mary Johnson.
When your Dad had his DNA done, did he have his maternal (mtDNA) or paternal DNA tested? My mtDNA test showed no Indian blood, so I thought it might be on the male side.
Also, I heard that it was William Shaw who was chased off. Maybe Onacata chased them both off! I haven't been able to find William Shaw either. The men didn't fare too well back then in this family, though having a house full of your children and their spouses and their children couldn't have been easy. I think the war really took a toll on all of them.
I've attached a picture of my grandmother so you can see where I might get the idea of Indian blood.