Look at what you wrote at the bottom about Henry Simon Gay. There is no way he can be the son of Henry III as he would be 109 yrs. old.
Henry Simon Gay is the son of Simon Lee Gay (b. 1755-1760 Edgecombe Co, NC) (d. aft. 1820, Irwin Co, GA) Simon Lee's parents are a mystery, but most list him as a son of Henry III, which would put Henry III in his 60s when Simon was born, and Simon is not listed on Henry's will.
Everything prior to Henry III is correct.