Based on the advice here, I think I will do this trip in mid June. Two weeks should give us enough time that we won't be rushed, and can explore off our route when opportunities present themselves.
I have just about firmed up my loop, and it looks like this:
Fly into Atlanta, GA
Myrtle Beach, SC
Fly out of Atlanta, GA
I'm thinking I should get an ADV sticker for the back of the rental car, just to see if I can get some salutes...