I am not in Texas, so I can't direct you to a specific place, but this is how it is in the Chicago area. There is a program called TRAP AND RELEASE. for feral cats. The organizations involved are ANTI CRUELTY SOCIETY, PAWS, and maybe a few more. They are GREAT ORGANIZATIONS........ You bring in your feral cats, they get fixed, and you take them back. You care for them after surgery, and feed them. They do not want to leave your area after they know where dinner is served. THEY NO LONGER MULTIPLY AND POSE ANY OTHER OVERPOPULATION ISSUES. The program is a SUCCESS. In previous times, catching and killing cats only promoted new cat litters to fill in the void left behind.
Feral cats can eventually be tamed. Yes, it is a challenge, but young kittens are much easier than adults. I have tamed an adult SUPER FERAL cat, to the point where I was able to pet her anytime. At this point she was spayed already. She ran away from strangers.
I suggest you try and contact HUMANE SOCIETY. in your area and ask them if there are any options for getting reduced surgery for these cats. I know money does not grow on trees and you do need to get all those you have fixed. I have read all the above posts, and they have given you good advice. Opt for eliminating them as your last option.
All the cats running around my home are fixed. You can see in my Avatar that they do not bother my chickens ether. They will live out their entire life here and they do get fed well. I have a soft heart. I also have no mice.
WISHING YOU BEST.