Tommy,
Beaverhead would be an excellent choice, Jack lives in the Gila and so do some of his guides, The best elk hunters I know are his guides, The Gila is going to be a premier hunt next year we have got a lot of rain.
Also Derrel Welty is also excellent, I own ranches in 17 and 21 and he is the best in these areas.
New Mexico will be super for a number of years with the positive changes that game and fish is doing to bring up the trophy quality.