Greg, I believe that I have some information that may connect my Aikens to yours.
A Peter Aiken of Newberry Co., South Carolina married a Nancy Pitts in Newberry Co., South Carolina.Their children were William, Pathenia (married Poland R. Daley), Patsey, and ANN AIKEN (married RIX AUGUSTUS RANDOLPH.)Ann Aiken was born in 1812 or 1813 (based on 1860 Butler Co., Mo. census and 1850 Hardin Co., Tn. census) in S.C. (1850) or Tennessee (1860 statement.)
Ann Aiken Randolph's parents Peter and Nancy Pitts Aiken also lived later in Hardin Co., Tn. and died there before 1838.I would guess that this Peter Aiken would have been born no later than about 1788.Rix (Ann's husband) was born in 1796 to John and Cloey Randolph in Virginia or North Carolina.
Notice that AUGUSTUS was a name given to a Randolph in 1796.Now that I have seen Augustus in your line, possibly from the Aikens, I am really wondering where that came from and what the Aikens and Randolph relationship might have been.
Okay, if your Nancy Aiken was born in 1791, as the 1850 census indicates, I believe your Nancy would have been a sister to our Peter.I do think that Peter and Nancy's father was a Peter Aiken also, but need to research that again.
I have the Pitts line pretty far back and can say that Augustus was not a name they used.So, it likely had to have been from the Aikens or Randolphs.It is interesting to note that none of Rix's brothers named sons Augustus though.So, bottom line, I think there may have been a relationship of John (Rix's father) and the Aikens, perhaps Peter, Sr. or a brother named Augustus Aiken.