.338 Win Mag and 9.3x62 are the best all round choices for North America in my armchair opinion.

Over gunned for deer, but good choices for elk and moose and adequate in times of danger if it brown bear or grizzly territory. Good for running game/driven game as well.

.338 Win Mag is similar to the .338/06 which is a copy of the .318 Westley Richards, a great vintage choice in colonial Africa. Used by Bell and others for elephant and capable on cape buffalo. Great choice. Need I say I want one!

The .338 has wide choice of projectiles from 160 gr to 300 gr. An excellent range from 180 gr to 250 gr.

Certainly will perform at sensible hunting ranges.

I wonder if BLRs are available in .338 Win Mag? Would make a great choice for Alaska. My BLR .308 has a reasonable trigger shoots fast, is carbine length, lightish and is very accurate. Would actually make a fine mountain rifle.