I'm in NC, so take this with a grain of salt as to whether it'd work in Texas, but I was reading that some Nilgai get out of the expensive hunting ranches and are becoming a problem for some farmers. They are good at busting fences and reproducing.
As previous people laughed at my suggestion, you aren't going to get access to these farmers as a random person off the street. Start asking around your church, kids sports league, any other extra curricular/hobby group. You're looking for both farmers and for people with service jobs that interact with many new people on a daily basis.
I had a very interesting conversation with my termite guy. He's had wonderful success getting private hunting leases on land owned by non hunters, all because he asked the question while talking to the owners during their termite inspection, think about septic and well tech, HVAC, plumber, maybe even gardners, tax preparer, lawyer, etc. Find these people and build a relationship.
No, it's not easy, and it'll take many failed efforts. But it's not expensive.