I would go with a 44 mag, 444 or 45-70.
. . . or a slug gun.
This is where I'd go if I already had an accurate and reliable 30-06 for all around hunting.
My reasoning is based on the fact that no matter where I go hunting in Alaska, there'll be the chance/need to take a bear. And a 30-06 will work well. Going smaller than that can be okay but that's starting to walk a fine line. 308/280 with vetted premium loads, okay. So something less and notably different than 30-06 would only be chosen if going to the range for fun. Then looking bigger than 30-06, and we have to go quite a bit bigger to make the step worthwhile. Either 338 win mag or 375, but the recoil and/or the weight is a big increase and there's nothing up here that those can do that the 30-06 can't as long as you do your part including skillfully moving within 200 yards of your target. But then there's the role of a handy rifle that can stop a bear when you're not necessarily hunting. If I'm spending a lot of time in the field, a handy defensive long gun that can take a lot of exposure to weather and dirt is what I take.
