I also live in Easley,SC. I have a Hunnicutt Line well 2 actually. I have proven Mary Catherine Hunnicutt who md. Thomas Franklin Dodd back to William & Mary Hunnicutt from Oconee County,SC. But the second Hunnicutt Line of mine is Amanda Hunnicutt b. abt 1824 in Oconee County,SC. She married George W. Dodd son of Thomas Franklin & Mary Catherine Hunnicutt Dodd.
My Amanda had a sister possibly a twin named Martha Hunnicutt b. 1824 living with George & Amanda Dodd in 1870 This is where I dead end. (I feel strongly there is a connection somewhere)
You mentioned a Robert Dodson there was one here in Easley that did alot of Black (Race) genealogy stuff. He is now dead. My Hunnicutt line is of the white (Race) If you think there is a connection please let me know.