I just got back form the area around Holloman AFB. As for the dog hunting, I would get something more than a 12ga. A .223 or 22-250 if you want it for double duty try the 243. But you need some thing with a little more range. The dogs have been called and will hang up outside of 12ga range.
The mountain west of town has BLM and NF, this area does have some dogs. You might want to check out the north area around La Lutz.
When i call with a partner or even alone i often carry or partner does, a 12 ga with no4 buck for the sneaky ones. Generally who ever is calling uses the shotgun or if alone i simply have it next to me.
Never waste your money on those distress calls, Lick the back of your hand and kiss it at an angle and do it nice and long and switch it up a bit. Sounds EXACTLY like a rabbit. Hasn't failed yet for me. Are you at camp roberts? When I was stationed at Ft. Hood we could declare our rifles at the gate. You can store your rifle with the help of your armorer. Belive me, I had to do it, and your captain will get pissed cuz they have to do a sensitive items check 3 days a week lmao
Try the Hevi-Shot Dead Coyote. I've used it successfully on Wisconsin coyotes out to 70 yards with a superfull choke in a SBEII. It gives you 54 pellets of T Shot.in a 3.5" Shell...a few less in a 3". The stuff is lethal.
Over the years I have seen several elk and deer hides left in the woods by hunters and I have to wonder why they do this? I fully understand and agree about getting the hide off the animal as soon as possible to cool the meat, but why not pack out the hide with you and use it? As far as I know there are no state laws that require you to take the hide home, but to me why waste such a beautiful part of the animal? Some might think they have no use for the hide or it costs too much to tan....