From Houston, it's about 14 hours (plus you lose an hour due to time changes). We leave from Shreveport and it's also about 14 hours. If we leave after school, we stop at Daphne, AL, on the east side of Mobile Bay. (that leaves about 7 hours to go) There is a Comfort Suites and Hampton Inn there. Both are pretty good. If we leave in the morning, we can get all the way to Tallahassee or even to Lake City. Also lots of good hotels there, but if you get there on a football weekend, you better make sure you already have a reservation.
When you get to BR, make sure you go on I-12 and don't go I-10 to NO. You pick I-10 back up at Slidell.
If you take the tollway, get off at Leesburg and take 27 to 192. You will totally bypass I-4 which is a mess most of the time, plus save some tolls. You come in the gate back by AKL if you are staying on the property.
One time we left about midnight and got to WDW about 3PM. Just in time to check into the hotel and take a short nap or swim.