I already posted on your other question on Disney Family. But we either take I-49 from Shreveport and down to I-10/12 or I-20 to Jackson MS, then HWY 49 to Hattiesburg, then HWY 98 to Mobile, hop on I-65 to avoid downtown Mobile and get over to I-10. Spend the night in Daphne AL, just across the bay from Mobile (when we leave after school, instead of first thing in the AM). Then bop on over to WDW the next day.
We did leave Shreveport at Midnight one time, took the route through MS, got to Mobile about 7AM and got into WDW about 4PM. Not bad, we were able to check into the AKL and relax there before we hit the parks the next AM, bright and early.