The late season cow hunt for 34 is limited to anything west of 6563 (Sunspot Highway), North of Cathy Canyon and South of the Apache Reservation. With that limited space I would park myself in the area around Haynes Canyon Southwest towards Westside road. Still a bunch of good country.
I live in Cruces as well and would be more than happy to show you some areas on the map. I just wish I was quick enough to get a tag for 34. PM me if interested.
A perk of majoring in wildlife biology in college is the plethora of hunting knowledge that you collect throughout your course load. One of the most important factors in whether an area can hold large quantities of animals or produce large antlers is forage.
Most universities, state schools and even community colleges offer basic botany courses and plant ID courses. Although it might not be feasable for the average middle age hunter to pay tuition and go back to college to learn hunting...