I used Regina Valley Wild Game Processing which is just down from Gallina towards Cuba on HWY 96 shortly before the hard left at the intersection of 112. The owner's name was John Schultz (575.638.0377). I was quite pleased with his knowledge of the meat cuts especially and helpful advice considering I am from South GA. If I remember right I dropped my elk off early in the morning and had it by mid afternoon so he can definitely work on a schedule if required.
1321 Highway 96
Regina, NM 87046