dirty: If you want to carry in NM, get an AZ permit. I got one a few months ago just to add to my collection, and the process was straightforward and efficient.
My philosophy is to obtain every permit available, even if it simply duplicates states you already have. In fact, my VA, NH, FL, and PA permits are technically superfluous, but they're insurance against states' whimsical changes in policy.
Of course, you don't apply to states that will turn you down certainly (NJ, NY, MD) or even probably (MA, RI).