That is our normal route also; sometimes we go on down on I49 to pickup I10.
Some alternate routes: US 80 (take exit to Elmo, TX past Terrell) if you are not in a hurry. We make just as good time, but goes through many small towns then through Longview and Marshall; past Marshall join I 20 just past Scottsville, TX)
Altogether different: take US 175 to Jacksonville, TX then US 69 to Rusk where you would pick up US 84 East to Hattisburg, MS where you would join US 98 on into Mobile. (There are several variations to this route but you would go through Farriday, LA and Natchez, MS worth a stop. Riverside RV a great stop on the Mississipi) I have towed on all these roads.
Not recommendations, just some observations.