Having killed good-sized elk and of course deer with the 6.5x55 and 7x57, I see no reason why the 7x57R and/or 7x65R wouldn't be perfect for what you envision.

"Out West" here there are certainly places where 200+ yard shots are pretty common, but overall most shots will nevertheless be within 200 or can be made that way. I myself have a self-imposed 200+/- yard limit on what I'll shoot. I practice too much at 200 yards to know better than to shoot much further!

If all you want is speed a BAR in .338 Win Mag should fit the bill nicely!