I have only been here for a couple of years so I am stiil trying to figure things out myself. This year is my first season with a tag. Not in 16 though. The game commission opened up a new unit to elk hunting and I have one of the 10 tags. No game carts allowed in the wilderness so it is on your back. I have not been able to find just a packer. The outfitters want you to purchase the whole enchilada and they pool their resources to bilk as much $ from the non-residents as they can get away with. The good news is that you may not have to go out as far as you may think. The outters have their usual campsites staked out and they try to stay away from diy'ers. Some boots on the ground scouting will tell you what areas the outters are using. Then figure out where the elk will be when the outfits show up. Been my experience that game animals tend to circle around behind the pressure given the habitat.
I have a friend nearby that will help me get the elk out should I be so fortunate. The larger bases usually have a sportsmans club....trap, target and archery ranges. Ask around their haunts. Also, local taxidermists might know people who go out and cape, pack out. In addition, check the game fish website for the open gates program. There are a few, not many, land owners in that area, who grant tresspass to elk hunters for access to the public land in the Gila. Good luck!