We live in Shreveport and just got back on Sunday. We took I-20 to Meridian, then 80 to Montgomery, then 82 to I-75. I-75 to FL turnpike. It wasn't too bad, just 80 and 82 are only 2 lane roads much of the time. And at night, there were a lot of deer on the road.
When we go in Jan, we're going back to I-49 to I-10/I-12/I-10 to I-75. The interstates are better and with at least one lane in each direction open over Escambia Bay (near Pensacola), we should be fine.
From DFW, take I-20 to I-49 in Shreveport. Then head south to I-10 at Lafayette. Don't go through NOLA, but bypass on I-12 (saves a lot of time). Hook back up with I-10 at Slidell.