Jak leaves to stay with his new wife, but that was in New Mexico, not Louisiana. If I remember right, when the jumped back to Louisiana and found the desert, they didn't stick around. When they got back again in Strontium Swamp, wasn't the desert still there in the area around the redoubt, but ended a couple miles out from it?
I do remember that the redoubt in Neutron Solstice was a ways off from where they met up with Jak (they hiked and then traveled by boat for a bit, with one of their original group getting killed as they were leaving on the boat).