Randi...just happened to stumble on the Hames site and saw your message. I too descend from this family and many years ago researched it. There is an entire book on this family (actually two volumes)initiated by a physician named Hames in Atlanta (I think, I'm going on memeory here). It's quite well done. Probably local genealogical societies (Broad River) have a copy or the local library or SC Archives.
In a nutshell they are English, like many of english descent in this area, they came from Virginia (Northern Neck area) and some branches have changed the name. They migrated southward into the wilderness and landed in this area. My group in the 1800s moved across the NC line to Rutherford County. One intersting note, they are listed in the Shotwell Papers (the story of a Col Shotwell who returned to NC following the Civil War and tried to resist the carpetbag government thru vigliantism...read KKK). don't feel bad cause virtually everyone who was anyone wound up being listed as a defendent...my group got banned from NC for a year and moved briefly back to SC. There is a "homeplace" for the Hames with a cemetary and it's located 10-12 miles below Gaffney. Try the Heritage Books for tht area, they aren't particularly hard to find.
Mu Grandmother was a Hames and all of her many siblings that I knew were farmers, conservative, generally successful, Baptist, hard working and handsome. Even into their old age, thye stood straight and had a twinkle in their eye. Good luck, Larry