After pouring over census records for Franklin and Banks counties from 1820 on, I've come up with a list of candidates who might be siblings of my ancestor James Hill, or at least related.
The 1830 Franklin County Georgia census lists the following:
Thomas Hill (born 1771-80)
James Hill (1801-1868)
Anderson Hill (1806-1884)
Caleb Hill (1810-after 1850)
James and Anderson are listed next to each other, and listed four homesteads away is Caleb. Thomas is listed within a page or two of this group.
The 1840 Dist 284 Franklin County Georgia census lists the following:
Thomas Hill, James Hill, and Levi Garrison (married to Nancy Hill b.1803). Dist 284 is now in the northeast area of Banks County.
The 1840 Dist 208, Franklin County, Georgia census lists:
Anderson Hill (apparently living in the same place as 1830)
William R Hill (1812-after 1850) is listed next to Anderson Hill
The 1840 Dist 265, Franklin County, Georgia census lists John Hill (1812-1894).
Based on the above information and some other nebulous circumstantial evidence, my hypothetical family for my James Hill consists of:
Thomas Hill (father) (abt 1775-before 1850)
Elenor Hill (mother) (1780 VA-after 1850 GA) (listed with William R Hill in 1850)
James Hill (self)
Nancy Hill (sister)
Anderson Hill (brother)
Caleb Hill (brother)
William R Hill (brother)
John Hill (brother)
The 1830 and 1840 census records for Thomas Hill imply another daughter and three more sons, whose names I cannot even guess at, only approximate birth years.
A current goal of mine is to track down descendants of Anderson, Caleb, William R, and John and get them to do Y-DNA testing through hilldna.com. This will either prove they are not siblings of James, or prove they are related to James (though not exactly how). With several names for a family, it is my hope that I can support my hypothesis that Thomas and Elenor are their parents, and possible find ancestors for Thomas.