I know Chama isn't that close (about 2 hours North), but Carnivore's in Chama does an excellent job (505-929-3133). Triny Vigil runs the place with his wife. The work area and coolers are spotless and prices are really good. He has been open several years, and is highly respected in Chama.
Vigils In Española. I’ve taken many elk, deer and domestic sheep to them. Price will be better than Abq and Chama and the quality is always so great. Cash only business. Have him make sausage out of a portion of your hamburger and you won’t regret it. It’s free and soooo good.
I have also taken meat, both wild game and cattle, to Vigil's in Espanola and was happy with his processing. One thing to note, he doesn't have much freezer space, so once he calls to let you know your your meat is cut and packaged, you need to be able to pick it up ASAP.