Don't know how much Brownings go for up there, but if possible I'd get one of those new fast-twist .22-250 Predator X-bolts (synthetic camo stock, medium-weight/length barrel), then load up some lighter bullets for gophers and also the heaviest ones that will still fit the dbm for coyotes.
Then again, I hear you can buy Tikka Varmints chambered in .243 up there. I'd own one of those for longer-range 'yotes in the wind (you can hunt wolves, too, can't you?); and also one in .204 for varmints.