Okay, I am going to go in a bit different direction. First, let me say that all the calibers mention so far would all make for an excellent sheep rifle. Having said that, those mountains that hold the sheep are also crawling with big, brown and ugly bastards that would make me second guess my favourite 270. Therefore, I vote 338-06 or 35 Whelen.
A 180gr at 2950 or a 250gr at 2500 sounds a lot better then a 120 at 3200 when it comes to a showdown with yogie. That 180 would still make a great sheep load; zeroed at 200 puts you only 12" low at 400.
Mind you, I might think twice about pulling the trigger with a 250gr at the bench in that ultralight. Ouch.