OK, just for consideration. This relates only to the route through Texas. I will assume Texarkana as a starting point.
Take US 59 to Marshall, TX. Then TX 43 to Henderson, TX. There pickup US 79 all the way to Rockdale and intersection with US 77. Take US 77 South all the way to intersection with I-27 very near Corpus Christi.
Yes, lots of small towns, a few bypasses, but NO Dallas, NO Waco, NO Austin, NO San Antonio.
This is the route I would take and I have been over every mile of it--not all on the same trip, as I would not start in Texarkana.
I will admit to a bias: I hate driving through major cities (though I have don it many times, including every one of those Texas cities I have named. I enjoy the more relaxed towing on US and state highways. But that is a personal decision.
This is the basic route already mentioned by my East Texas neighbor:
Mount Pleasant TX, Tyler, Palestine, Rockdale, Victoria, Corpus Christi.
Except my route even avoids Tyler.