I split in two days (coming from the Pee Dee) and typically go through Alabama (Montgomery & Mobile), New Orleans, into Houston. To me, better than driving towards Shreveport. Montgomery to Mobile is tough, but the gulf coast drive on I-10 makes up for it, a bit. About half way for me is Opelika/Auburn and have stayed there.
With you coming from Greenville , you can reach Montgomery easy, maybe Mobile, if you push it. From Mobile, you can be in New Orleans by lunchtime, and Houston by supper. If you find lodging in College Station , it's 93 miles to get there. Remember, the speed limit increases in Texas, so a little time can be made. And be aware Louisiana Troopers are waiting at the state line.
There are a few places to drop of I-10 along the coast for a scenic view, if you have time to spare.
Shreveport is a straighter shot but a tedious drive with not much to look forward to except crossing the Mississippi river, and then it gets even more bleak.