Welcome to BGH,
As you can see there are a lot of folks around here looking for New Mexico advice. Stick around, maybe someone will pop up for you. All I can offer is how I would hunt the area, but never have.
Looking at the unit, the first thing I noticed is the number of roads. It's kind of difficult to find a spot that won't have much traffic. It seems to me that the Canjilon Mountain area might be your best bet for a combination of water, cover, food and roadless space. It's fairly high elevation, but as gentle as ground will likely get in elk country (elk don't like to work hard either). So that's where I'd start.
Everyone has different ideas about trophy pictures. Looks around and you will see "long armers," "set behinders," "big cheesers," and "blood covered brutes." I have a few tips to keep your trophy pictures from being laughers or worse yet just plain gross.
#1 Clean it up. Try to avoid bullet holes, gut pile, mass amounts of blood, and the tongue sticking out. You don't want your big buck to look like a angry 1st grader with his tongue out or a MMA fighter during the 3 round.
#2 Long arming...