I've done it many times, down I-10. We did it both ways this summer. We've never stopped at Gulf Shore tho, thought about doing the state park one year but they had a three day minimum stay. I-10 itself is fine. LA or MS always, one or the other or both, have the road torn up near the Mississippi river bridge. So it seems like there is always a traffic jam, the east bound lane was backed up for miles when we went thru going west.
Stay on I-12 when you get near New Orleans, it connects back into I-10 on the other side. I-10 thru Florida is flat as a board and a straight board at that. The most exciting part of the trip is the tunnel at Mobile.
You are doing the most boring part of our summer trips out west. I usually just go as fast as possible not expecting anything good until we get past San Antonio. We tried a couple of days in Louisiana the summer on the way back. Took the Tabasco tour and so on. Ate some gumbo at a highly rated restaurant. But we both felt it was not worth repeating.
BK