Searching for anyone's parents prior to 1850 is difficult. There were no birth records in South Carolina that early in time.
I'd look for his marriage record. That might have both sets of parents. If you find it but parents aren't listed, then I'd look for the newspaper announcement of their marriage.
I'd also contact the Jackson TN genealogical & historical society to see if they have any info about his parents. They must have a local death index. Ask if they have newspaper death notices indexed and cemetery inventories.
Since you know when & where he died, you can look for his newspaper death notice. I don't have TN newspaper info but you can do a Google search and find it.
Look too for land purchases. George might have purchased land from his parents. Successful Searching!