Louisiana
Louisiana Tech
Tulane
All 3 should agree to schedule each other every year on a perpetual home and home basis. We would have our own little in-state conference schedule. We could come up with a special trophy for the school that wins both games to never relinquish bragging rights as state champion until another school wins both games. lsu would be more than welcome to enter our in-state conference if they want.
If we are not going to schedule a home P4 game, this is the next best scheduling strategy. This would be VERY popular with each fan base and seen as a very good thing by the rest of the country.