Check the Albuquerque Journal now and then and I also believe the game and fish website lists at least some land owners. After they screwed up the hunts a couple of years ago things have become even more difficult
I missed a landowner tag by a few hours just the other day. It was $1500. That is just the voucher, you have to pay the state tag fee to New Mexico Game and Fish as well.
It’s probably too late for this year, but one strategy could be to contact landowners using onX info (or drive around knocking on doors if you have time) and ask to hunt the last hunt for whatever you’re willing to pay.
I’m from NE New Mexico originally and most small to mid-size ranches don’t seem to sell tags for all three hunts. They’re still selling to people that hunted on them before the tag allocation system changed and those people want the first hunt. This will be my third year in a row hunting a buddy’s place the last hunt. We have it to ourselves and we’ve both killed opening day the last two years so the last hunt is still a good one. The bigger ranches often sell their tags strictly through an outfitting service.
Edited to add I see people charging $1k to $3k. I’m lucky and hunt for free aside from some gifts for the family.