I can help on your Polly and Alexander Walker as my wife and you are related. My wife, Polly, descends from your James' sister Elizabeth who married Reuben Patton and they too went to Madison County, Ark. Two daughters of Reuben and "Betty" married Sullins brothers and one couple were grandparents to my wife through a Sullins daughter.
Alexander and Polly (Allen) Walker were in Perry County, Ky in 1850. Children were Nancy,Elizabeth,Mary,Martha,Cynthia,James, William. By 1860, they were in Breathitt County County, Ky. (where Reuben Patton and his orphan siblings lived) Added to the Walker family were children Catherine, Benjamin and Lewis.
In 1813, Christoper Walker married Elizabeth Stewart in Knox County, Ky. They were the parents of Alexander. They were in Madison County, Ark. by 1860 so preceded Alexander and Polly there.
Elizabeth (Walker)Patton died quite young and Reuben remarried to another lady from Floyd County, Ky, Nancy, a widow, nee Prater but all his children were by Elizabeth.
I think I can give you Polly Allen's ancestry but that will take a bit more checking in my files. Did you James go to Arkansas??