Train to Bham from NOLA is $54. You could certainly get a rental after that, drive the 2.5 hours, and have a car.
i lived in hotLanta for a few years & alotta us liked that option..
FOR the record on flying there: Hartsfield, as the Delta home/hub, seems to play games--
i've always thought they over-booked & over-priced fares quite often;
Seemingly made no sense:
a few yrs ago, i bought a last-minute ticket during holiday-rush
& was cheaper than the prices i'd paid for a year or 2 leading up that that point..