Hey, finally something I know more about than many members! I lived in Las Cruces for high school and college, then moved back again 2005-2017. Did a lot of work at WSMR and Holloman AFB. Driven on most of the range roads. Even built a village of a dozen CMU block buildings on the eastern side, with an underground tunnel between two of them. Southern half is patrolled by WSMR Police with radar guns and they will give you speeding tickets. Ask me how I know... North half is (or was at least) patrolled by rent-a-cops without radar guns. But you need to be careful, because roads are varying conditions and sharp corners come up fast. Don't expect cell coverage, and have a jack and good spare... A friend has worked out there as a biologist for years and seen a lot of things and shown us pictures. Believe it or not, there are black bears in the mountains! Also crashed missiles, ruins of old ranches before the govt stole the land from them in the 40s, and Indian artifacts and petroglyphs all over. There is still UXO out there in random places, but I've never found any even building miles of tank trails, roads, rebuilding 14 wells all over, etc. Trophy hunts might have a game warden, whereas ours usually had a sponsor, someone who works at WSMR and volunteers to guide folks.
I've harvested 3 oryx, my Dad 6 of them. All depredation hunts. Dad has a 42" bull on the wall and a matching 41" cow. I had my first one, a 36" cow shoulder mount done. That was actually NE of the range on BLM property. My last one, part of our hunt area was closed due to the balloon program, so I got to hunt on the San Andres Wildlife Refuge, ironically. Most of the dumb ones are already in someone's freezer. Depending on what area your hunt is, could be mostly flat or some very, very rugged mountains equal in every way to Afghanistan minus being shot at with an AK... These days any animal without a broken horn is a trophy due to increased hunt numbers. The Army would like to exterminate them due to alleged danger of collisions, but that's pretty much impossible. They've spread west to AZ and down into Mexico already. Any female you shoot will almost certainly be pregnant. I forget the gestation period, but they will be preggered again a month or so after giving birth. They are also a lot more skittish than they used to be. While we used to always see groups of them along US70 between Las Cruces and Alamogordo, it's been years since I saw one from the highway.
Shots can be anywhere from 100 yards (unlikely and better be fast) out to as far as you can. You're not going to sneak up on them or chase them on foot. Shoot through that front shoulder. Go for the heart, not the lungs. Dad hit one in the liver and it ran for miles and miles, lucky we found it. They are extremely tough animals. We've dug other people's bullets from them when butchering them before. They are also tough to gut! Unlike a deer or elk where the guts practically fall out for you, these antelope have it all attached in there and you'll have to work at even cutting the diaphragm out. September will be quite hot, so take plenty of water. When you get one down, get it gutted as soon as possible to start cooling the meat. If you can't get it off range and somewhere to skin it out fast, take bags of ice in big chest to pack the cavity with. The meat is excellent, better than any deer and better than elk but very, very lean. Cooking it too fast, too hot will make leather though. I've used meat we vacuum sealed 8 years later and it's still good. Congratulations and good luck!