I have no researchable data to share, but am very familiar with those last names in that area of Louisiana, from the stories of my great grandfather, who,like most of his family was illeterate...so maybe his oral histories will give you some clues. First off, I think Buxton is a supposed Melungeon name, or Redbone as we say back home, and you can look that up if you don't know what it means. So, with that said, it would tie your Buxton and Doyles together, as well as my Thompson family, which is directly related to the Doyles. Further it suggests a fairly heavy native American heritage, mostly thought to be either cherokee or other indian from the area. (there is actually a small Clifton choctoaw community near gardner which is just west of Alesxandria on highway 28 which is right in that area) Doyles are first cousins. The branches of both those families lived near Alexandria, Louisiana around Glenmora, Oakdale area, which is VERY RURAL. Most were involved in timber industry. Some of the grave yards are unmarked and not known except to family. Occupy #1 Primitive Baptist Church and Occupy #2 with their graveyards may be findable in google maps, but they did not even have electricty there in the late 80s with any reliablity, but there is another that I have not seen since....maybe the mid 70s? It was located near Cherry Winchee creek.( and I suspect was meant to be Cherokee Wench).Not sure of spelling, it was a dirt and gravel road then. and it was on the side of the creek and had graves that went back pre civil war. Family there included Doyles, McGintys, Thompsons, I dont remember any Buxtons, but I was young, and also GOINS (which is actually pronounced GOOOOinns by old timers.) The Goins also have a large family group near the the Pollock area, including their own family cemetery off of Dyson Creek Road if I recall correctly. I also know that the family tends to be very closed mouth about their heritage, probably due to the illeteracy and the mixture of races as being part anything but white, indian or otherwise, was considered very shameful. The earliest THOMPSON ancestor I can recall ever being spoke of was BLACK JACK Thompson. Jesse Doyle is the earlies DOYLE I can recall. Aunts Bess and Birdy were Doyles if I recall correctly. Not sure if any of this helps, but I do hope so.