We drive down there just about every month pulling the camper.
I've been just about every direction you can think of from north alabama, and my favorite with the least traffic problems and the best time and best gas mileage is I-65, I-20, I-75, Turnpike, 429, Western Way.
As I said, I've tried them all - I-65 to 231 to I-10, I've also gone I-65, then down through Auburn, then picking up I-75 in South Georgia, and I've even driven to Chattanooga to I-75 there.
We now leave Huntsville late afternoon and take I-65, then go through Birmingham, then onto I-20, then through Atlanta well after 7pm, then stop for the night somewhere in Tifton, GA, then onto WDW the next morning.