257 Bob Imp!
257 AI is the way to go in my opinion. Easy on the shoulder for shooting, will reach out there, and won't break the bank on reloading. As someone early on said, I'd go there.
6.5-284 would be my next choice, personally. I currently am in the end stages of a 257 AI build, about to start a 338'06 A-Square, and am thinking about a 6.5-284 or 270 WSM next.
270 WSM would be a great choice for you also.