Well, after a whirlwind week or so, I am here at College Station. The route I ended up taking was US-59 to US-190 to TX-30, which was slightly longer than what's posted above, but it had more four-lane mileage.
The drive overall went pretty well, although there was quite a bit of traffic through Chattanooga. I ended up spending the night in Forest MS, a smidge past the halfway point, in the ABVI, which was okay but not as good as its reviews suggested. The next day, yesterday, I drove the rest, which was also uneventful, except for the random thunderstorms that would pop up from time to time. Driving through them was sometimes difficult, especially with respect to visibility, but they did keep the temperatures down.