Look at early records in Martin county, North Carolina.
According to the 1790 census, only one adult Brogd*n with the given name of James was recorded in North Carolina. He resided in Martin county and apparently had 6 children: 2 sons and 4 daughters.One son was 16 or older and the other was under 16.The year 1775 (the year you give as the birth year of James S.) is close enough to the age boundary of 1774 (1790-1774=16) that the older son could be your James S. Brogdon.By 1810, no James Brogd*n appeared in Martin county.The only Brogd*n in Martin was Susannah. She was likely Susannah McHenry, the widow of David. He was the only other Brogd*n in the 1790 census in Martin county.He is thought to have died before 1800.
But there is more supporting a Martin county connection. In my database, I have "James Turner Brogdon" listed as being born in 1806 in Martin county, North Carolina with no parents as yet identified.And I show that James T. migrated to Alabama where in 1832 he married Polly Byars in Jefferson county and died in Tuscaloosa county in 1860. Adding this Alabama connection, it seems possible that James Turner Brogdon was a relative of your James S., maybe even his son.
In summary, we have some interesting points of coherence suggesting that your James S. may have come from Martin county, North Carolina:
(1) a James in Martin county with a son born about 1775. (2) James T. also from Martin who could be a son of James S. (3) James T. migrated to Alabama same as James S.
This is not proof but only a THEORY so please consider it as such.But it does suggest where you might want to do some more research.
Please let me know what you or anyone else finds if you pursue these clues.