Buying a new car/truck.

inventory availability is the biggest obstacle of course. There are a bunch of all wheel drives in New Orleans from what I see. I can only guess that they are just taking what they can get because I can't imagine those would typically be big sellers here.
Just a suggestion that may not pan out - if you just want a FWD, maybe see what the inventory is in some of the northern(er) states? I can tell you AWD are the most popular around here in MD, especially around this time of year, so you might be able to find some more inventory and pretty decent deal.

You could always get a one-way ticket on Southwest pretty inexpensively (a non-stop flight is 3 hours), and drive back - it's about 18 hours. Still, you might be able to save a little cash and get the car you want.

Be sure to check LA's registration for cars purchased out of state, especially regarding taxes, to see if it's even worth it.