4Weight,
I've drawn 6 NM deer tags in the last 6 years as a nonresident. I live a few miles from the NM boarder and only apply in NM because it is close and offers me an opportunity to hunt most years. Besides unit 3 (Jicarilla Reservation), your odds of finding a B&C deer in NM are minimal to nonexistent. 2B and 2A have too many tags which results in almost all of the bucks getting killed at a young age. 2A and 2B are not the trophy units that their draw odds reflect.
The SE part of NM isn't a bad option if you are just looking for an opportunity to hunt, just don't expect to find a buck to hang on the wall.
Hunting license in NM is nonrefundable and you have to front the tag fee. If you are happy with just having an opportunity to hunt, then apply in NM. If you are only looking for a wall hanger, take Cosmic Cowboys advice and look other places besides the NM draw.