thought I'd chim in
I'm from Atlanta (currently on the Trans Am); have ridden from Atlanta to San Diego, via the S. Tier; and also the East Coast, from Atlanta.. Here's my suggestion:
I would take the Atlanta Coast Route to Statesboro, from there, head west. Part of the reason is you'll be in rural GA, where services/camping should be better. Too, you can make a stop in Athens which is a pretty cheap town for a lay over if need be. There are good bike shops in Athens too, if you need one by that time.
If you end up in Athens, there's the MS 150 ride every year, from Athens to Atlanta - which is mapped. The routes not perfect, but it's out of the way of 78 or 316 which are both main stretches to and from Atlanta/Athens. By taking this route, you'll end right downtown Atlanta - at the capital. If you up for staying in Atlanta - there's a hostel there which is awesome (not well advertise in the US, strangely, but it's a good place - http://www.atlantainternationalhostel.com/
This should give you an idea of the MSA 150 route - again, the route was updated for 2012:http://www.nationalmssociety.org/chapters/gaa/fundraising-events/bike-ms/atlantatoathens/downloads-and-resources/download.aspx?id=40269
Once you get into to Atlanta, I would suggest heading south west - toward Columbus. There are a ton of back roads - grab a state road map, find anything that borders 85 (more services.)
When I left for San Diego in 2009, I took the silver comet trail to Alabama. Was fine, but, only after which, I had to cut through Alabama south to Graceville FL. Alabama's an awesome state (people are amazing - seriously) just that you'll end up doing the state-park tour (provide you want to camp) which isn't the easiest. Although, too, in thinking about it, rural Alabama is super fun.
By heading southwest toward Columbus, you'll be out of the metro-Atlanta area fairly quick, but too, can pick up the S. Tier in Florida faster south of Columbus, than you can taking the silver comet trail west, then south through Alabama - if that makes sense.
After you hit Florida - say in or around Defuniak Springs, you can follow the South Tier direct to Lousiana.
I'll try and check back in a few days. If you need specific info, or have specific questions - so me a private message,