I have a friend who went to grad school there. He killed a huge cow elk in the medicine bow mountains with his vintage early 1980's compound (not far from traditional, huh). He simply bought an ultra cheap resident elk tag and started walking around on his lonesome on the public land for days at a time with only a GPS. Packed it out in 4-5 trips. He didn't know a thing about what he was doing with elk... and managed success. September is best though, before things get crazy with gunners later.
After a few years away, he loved it so much he's chosen to move back with his family. Maybe one day if he gets some free time and I can persuade him to get into real archery, you could meet up.
I'm certainly hoping to make a trip out there one of these years to go after a beast.