Are you a member of Long Range Hunting . com. It's more geared toward hunting, and especially out west. Join, and throw this out to them.
With the time constraints and budget, you'll just about need someone, or a guide to take you where you want to go, if you want any shooting time at all.
Western SD, WY, Montana are a little different than where you're coming from, there's just not a road every mile, thousands of acres of land are unviewable from a road, so you need an "in".
You're best bet would be to come out this way, spend time looking and meeting land owners with P-dogs, and develope some relationship for the next year. I'd steer clear of the Indian stuff, and really wouldn't pay anyone to shoot them, there's plenty out there. Any public land with dogs gets hammered all year long.
And like VS said, 3rd week in June is optimum. They like sun and heat, but not mid-day July heat.
As for your gun selection, it is what it is, but bullet speed is what makes this game fun. A 22-250, .220 Swift, .243, fast lite bullets= air time, lead induced acrobatics and such. Watching someone else shoot one sometimes is more fun than hitting it yourself.
