Your area and mine are very similar. I lived in Lafayette area for nearly 20 years and drilled some oil wells near Ragly and Dequincy. Geology and plant life are almost identical to mine except my area tends to be flatter.
Both our areas, at one time were part of a vast longleaf pine forest that ranged from Mississippi to about 60 miles west of me. It was different than what we see now. No brush under the pines--no direct sunlight fell on the forest floor and historical accounts say it was like walking in a well manicured but huge park. Trees spaced out 30-50' apart and the ground a carpet of fallen needles.
When the timber companies moved in during the late 1800s and very early 1900s, they clear cut all the old growth longleaf, then replanted with the much faster growing yellow or loblolly pine. In the interim, invasive plants had a chance to get established since sunlight now go thru. That's also how all the sweetgum and oak got established and later, the tallow.
No, I know of no forage that will choke out a tallow seedling. They are the the top of the plant life food chain for your area and mine. Only thing that comes close is sweetgum in our areas. You can mow them tallows from now till the end of time and you won't kill a single one. Cut one down, and the stump will sprout out a dozen saplings within one growing season, and those are the very hardest to get rid of. Frill cut and spray a mature tallow at the wrong time of year, and the tree will die, but it's root system will send up 1/2 dozen new ones to take it's place within a 20 yard radius of that now dead tree. Cut it with a chainsaw in spring or early summer, sap will push off any Tordon you treat the stump with, meaning the stump will not die and neither will the roots. (You want to do the cut stump treatment in very early fall, before the leaves begin to turn colors--Sept-Oct and you will need to apply the herbicide within minutes of cutting or frilling)
I'll try to get a few pics tomorrow of a couple I "killed" back in early spring this year.
And yes, I had cattle grazing mine most of the time since I cleared the land, but kept them in the wooded areas for several months while my bahia and bermuda was establishing. The invasives however, sprouted up within weeks of clearing the land, and even moreso after I tilled the new ground.