I have a theory who he belongs to... sort of. I've been trying to track down the Wayne family of Hancock Co., GA. In 1820, two Waynes are listed in the census. 1) John Wayne who moves to Hall Co., GA and established the line that I've researched. 2) Thomas Wayne - who kinda just disappears.
Examination of GA lottery records and marriages, some other names pop up as well. William (who I believe is the father of the two above), Green (who disappears then reappears in MS in 1860), and James (who I believe is your man).
There is a record I have buried in a file that was a resumption of guardianship c1849 by James Wayne in Hancock Co., GA for his two daughters after the death of his wife. He had apparently gone to Montgomery Co., AL having left his wife and children behind. He had returned to take them back to Alabama. This record prompted me to se if there were any Waynes in Montgomery Co., AL and I found the James W. Wayne, father of your Georgia Ann Wayne.
So my theory... take it for what it is worth... zippo.
William Wayne of Hancock Co., died between 1920 and 1930. He's listed in the lottery records, but not in either census. John Wayne has one person living in the 1820 household that is 50+, so I presume the William listed in the lottery must be that elder male.
His children include: John (c1797 - bef 1870 GA) [my branch] Thomas (no clue) - older than John, not listed in the 1830 census. Green (c 1803 - 1868 LA) -> progenitor of the Judith F (Wayne) Oxford line Sarah(c1800 - 1873 GA) m. Richard Foster Breedlove Anne (c1790 - bef 1821 GA) m. William W Breedlove
I believe that Thomas is the father of James W Wayne (Montgomery Co., AL) as well as William P Wayne (Walton Co., GA), John S Wayne (Walton Co., GA) and Thomas Wayne (Tishomingo Co., MS).
I believe that Green is the father of John L Wayne (Pike Co., AL), William Wayne (Neshoba Co., MS) and Green Wayne (Stewart Co., GA) based on census records and lottery records and likely ages as well as letters between Judith Oxford and her cousins (midpage at this link: [http://freepages.genealogy.rootsweb.ancestry.com/~oxford/johnhoward3.htm]). Although it's possible that Green is the son of Thomas.
But its all a guess. I have yet to find a decent record to prove my hypothesis. So, there you have it... a theory to chase... better than nothing.