You can search for Diplomats of the American College of Theriogenologists including contact information for them here:
If you search for those in Texas, you will get a number of hits.
Seventeen of those listed in Texas are also listed as active diplomats. Seven of the seventeen are listed as being in private practice. Six are listed as being in academia, and four do not list the type of practice.
Drs. Jasko, Niswender and Vest list equine as their primary interest and are in private practice. Dr. Wallace is listed as in private practice with equine listed as a secondary species.
The aforementioned Dr. Espy does not have a primary or secondary species listed.
So, if those data are current, you have your choice of among at least five Diplomats of the ACT that are in private practice in Texas with locations in Magnolia (Vest), Granbury (Niswender), San Antonio (Espy), Peaster (Jasko) and Gainesville (Wallace). Otherwise, you can go to TAMU and be awash in Diplomats.
But, you didn’t actually ask about those with DACT credentials. There are probably many vets and technicians that can handle your mare competently. Kathy St. Martin isn’t a vet and not a Diplomat of the ACT but I would put her up against any that is.
I believe Dr. Steve Van Wagner is good. He is in New Waverly, which is about 45 min north of Houston. I do my own AI with frozen semen and ET, but Dr. Van Wagner is who I use for other equine veterinary services. He is also the one who handles breeding for Jan and Gary Marquardt of Walkabout Station.
I should add another disclaimer: Dr. Niswender is a friend and former fellow graduate student. He is very good. Before doing my own work, I sent a couple of mares to him.
I trust Sonesta that Dr. Vest would be a good choice.
Best of luck.