Bob,Your post is appreciated.Your documentation clarifies the issues involved.The John A. Jones in the 1880 census may well have been of mixed race but he was not the son of Andrew and Rebecca Box Jones.
There were at least 3 different lines of Jones in the 1850 Clarke Co. AR census with a John Jones in the family but none fit the John A. Jones in your post and none had an apparent connection to Virginia.I know of no connection your John A. Jones would have to the family of Andrew and Rebecca Box Jones.
Beth Streu has a collection of 1850 censuses enumerating Rebecca Box Jones and her 11 surviving children which show that her son John A. Jones wasdeceased (the census of Clarke Co. AR shows his widow, Mary Ann Jones, and her seven children were enumerated adjacent to her brother-in-law, Robert Jones).And the pages from a Jones Family Bible included in the book, "The Family of John Jones 1755-1811"by Bobbie Jones McLane show John A. Jonesdied January 29, 1850.
These data do not prove the family of Rebecca Box Jones did not have a native American heritage.However,I have seen no indication so far of such heritage in the census data.
I do appreciate your post as every tidbit makes a contribution to our knowledge of our ancestors.