You could go I-55 to Jackson, US-49 to Hattiesburg, US-98 to Mobile, then I-10 to Jacksonville, and up I-96 the short distance to Jekyll Island. This adds about 280 miles to the trip.
But I'm not sure that going through Memphis is any better than going through Nashville, and have no idea how Jax compares to Atlanta, since I turn south just east of Tallahassee to get to my destination. I avoid Memphis by starting south at Little Rock on I-530/US-65, but that doesn't work for starting at St Louis.
The difference in mileage doesn't bother me much because I have stops to make on the Gulf Coast anyway, and no longer have reason to visit Nashville since my daughter moved away from there. When I was going through Nashville, I used I-65 to Montgomery, 231 to I-10, to get to Florida or southern Georgia.
Briley Parkway around the north side is one good way around Nashville, although the parkway is also crowded during rush. Last time I was there, it was freeway only as far as I-40, surface streets continue to I-24. Coming from the west and going south I-440 works OK some times of the day, but during rush hours it is badly overloaded and tends to get clogged around interchanges.