Welcome to the fight. Good group of mesquite busters here on the OB. You'll get some great advice. Have my hands full right now will try to reply later.
Edit: We have used basilar spray, canopy spray, grubbing, aerial, and cut stump. They all work, and all have pros and cons based on your property size, tree density and tree size, and plan/desired end use.
Sendero and surfactant in water is very effective, but you must cover the entire plant and get all leaves. Miss a branch, it will live and the tree will come back. So for bigger and taller trees, you end up wasting a lot of chemical in the air.
Basilar spray w remedy and surfactant works great too, but you need to mix w diesel not water. That technique works well for medium sized trees without thick bark and aren't so thick you can't get to individual trunks.
Grubbing works very well, but you have to get the tap root and know what you are doing. And also if you take the trees you have to schedule a burn. We've been in a burn ban for 2 years.
Cut stump - very rewarding. Nothing like cutting one of those sobs down w a chainsaw. But very slow. We do this in winter when it's cooler and snake activity is not a problem. Paint the stump within 2 minutes w a 25%remedy 75% diesel mix. Get it on cut surface and all remaining bark. Kill will be 95% plus. Wait longer than a few minutes to paint and your kill goes way down.
Aerial is the most niche in my opinion, as it knocks the mesquite back and does kill some. This allows grass to return in short term for improved grazing efficiency. But you'll have a lot of trees survive and come back 3-5 years after an aerial treatment. That's my experience in Coleman county. We are covered up w mesquite. Been killing them since 1997.