I've hunted that range successfully twice, once my buddy's hunt, once mine. The first was pre 911 so it was a bit more relaxed. We were even allowed to camp on the range in the Stallion Range Admin Building parking lot. They also provided a large a frame for skinning and quartering if needed. The next time was my hunt, the year after 911 and they were very tight on security. We needed to be at the gate a 5:30 AM, go through security with three agencies, and then on to the admin building for the mandatory orientation. Out to hunt about 7:30. Once an animal was down you called in and your hunt was over. You had to field dress, load and depart as ASAP with security guys watching your every move. The funny part is I got my animal 45 minutes in, we were out the gate, and I was home by a bit after noon (Taos area). About 5:30 I get a call from the Army wanting to know where I was? The guard checking us out forgot to mark us gone so they thought we were still on the base somewhere. Bet he got his ass chewed!
I've hunted off range as well, which are draw hunts.
Those
Oryx tastes good too!