In my response to your posting I made two errors: 1) I cannot repost your query and my answer as one posting.
2) Nancy in the 1870 and 1880 census record is PROBABLY Nancy (Gibbs) Slaton, not Nancy (Clardy) Slaton. This means that your line is PROBABLY from Thomas Slaton, thought to be on of the heirs to William Slaton's 1838 Pickens SC estate, William had married Sarah Honey. There is no clear way to identify between two Thomas Slatons found in records in the area, another appears to have married Ann Kirkland.
If you have 1900 and 1910 census records for Joseph(us) N Slaton please contact me. I have not found them at the time of this posting, but he and Alice should be in 1910 GA records.