I'd choose my Remington KS Alaskan Wilderness Rifle in .300 RUM with a 220gr Partition. Much lighter and easier to carry than my 375 H&H Sako and still has long range capability even better than a .338 Win Mag, with much less recoil.
JMHO. I chose the rifle I wanted first, & then the Caliber.

But in answer to the OP's original question, if I had to choose form the calibers he listed? I'd take the Ruger Hawkeye in a .375 Ruger. That rifle / caliber Combo ought to be the perfect choice for an all around Alaska Bear & Moose gun.

"Allways speak the truth and you will never have to remember what you said before..." Sam Houston
Texans, "We say Grace, We Say Mam, If You Don't Like it, We Don't Give a Damn!"

~Molɔ̀ːn Labé Skýla~