Fred don't know if this will help you but there were two other Thomas families that have Grundy & Franklin Co TN connections both of whom were in Fairfield Co SC in 1800 and possibly 1810. They were Jonathan & Richards Thomas who are believed to be brothers.It appears they were in Putnam Co GA briefly as Jonathan's son James married Miranda Walker there.
There was an Anderson Thomas (full name Matthew Anderson Thomas) in Chester Co SC who had a lot of sons who are not identified (he died about 1815-16) many of whom were born up to 1800 based on census info.He owned a lot of land throughout SC & some of his older sons (b. 1760-1770's) also lived in Edgefield & Pendleton Co, SC before they moved to GA & AL. Jonathan & Richard Thomas appear in neighboring Faifield Co about the time some of Anderson's younger sons disappear from his census household which is why I am looking at his line.
It may not connect to your George W Thomas but its possible so I thought I'd pass the info on.My line (Pleasant Rhiner Thomas) was in Tippah Co MS in the late 1840's & his apparent brother,George Washington Thomas was found in Chester Co SC in 1840, then Tippah Co MS in 1850.Pleasant's wife was born in Fairfield Co SC and was there when father died in 1835 so that is why I'm familiar with some of the Thomas' in that area.