I have used Carnivore's in Chama, and Cole's in Pagosa Springs. My problem is I drive to Chama then bring the processed meat home in ice chests packed with dry ice. I have to wait for the meat to be processed. Triny Vigil at Carnivore's no longer does any "rush" jobs and it can take up to two weeks to process your meat. He wants to vacuum pack everything (additional $$), then ship it to you (more $$). I used him once when he first opened but haven't been able to get him to do it after that since he has been too busy. I would use him because I stay in Chama before and after my hunt, but he is always backed up. His number is (505) 929-3133.
Coles Processing in Pagosa is a lot easier to deal with. Lindsay will take your elk if she has room and will do a rush job for $100. Processing is first class, wrapped in clear plastic wrap, then wrapped in white freezer paper. It is marked with the hunter's name, what is in the package, and the date. The meat is frozen solid when I pick it up. She is very easy to talk to and I have used her the last 3 years. Hopefully I will bring her another bull in October when I hunt in Chromo this year. Their number is (970) 264-2426.
Depending on which way you are heading when you leave, there is also a processor in Tierra Amarilla south of Chama. It is The Dam Meat Processing at El Vado Lake. I haven't used them but the owner of the Motel I stay at uses them regularly and highly recommends them. Their number is (575) 208-1733.