The Gila by me is pretty rough. No roads. Thick mesquite, catclaw, and brush make getting to the dogs tough. Scarce coon and ample skunks proved mighty tempting to my young dogs. Not sure what it looks like out west.
With that said where there is water you may find coons. Are you seeing sign? Please research the regulations but as they are not big game a bit of bait and a trail camera should be telling.

Found this area while Javelina hunting this spring. Tons of tracks up and down the road. Water and feed close by.

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This is a few miles away. My dogs treed all three of these rascals. They were much smaller than the others. Been wanting to get the dogs out but it is so damn hot!!! Maybe a nap and 2am start is in order...
PM me if you want to explore your area some or try the east side.