If you want something bigger then your 338 or 9.3X62, then make the jump to a 416, a 375 really isn't that much bigger, it is a large medium bore as opposed to the 338 that is on the smaller size of medium bores. The 416 is a big bore, or you could always go bigger, I sold my 458 lott to build a 500 Jeffrey :-D
As far as respecting natives, there lands and culuters, that is a very, very complex issue. There are about a dozen recognized different native cultures throughout the state. No disrespect intended, but I think the most important thing to realize is that there is no mystic harmonic link between the natives and the land, there are just folks like everyone else, there are some really fine people, and some folks you would have no desire to associate with. There is a Native Herritage center just off the base, and it is worth visiting.
As far as handguns, I used to carry a 44 mag super blackhawk, but replaced with with a 480 SRH, which I really, really like. I carried a shotgun for the first year, but have realized that shotguns are a poor choice for bear protection. If you're going to pack a long gun, make it a big gun, as you can only expect to get off one shot, and it best be something powerful enough to stop or turn a bear with marginal shot, which a shotgun can't do reliably.
There are certainly many times that a long gun just isn't practicle, but a pistol is easily carried at all times. I packed my 480 for at least a month in the woods last year, and with a good shoulder rig, I never noticed the weight.
Another range option is Rabbit Creek in Anchorage, it's a state range with pistol, rifle and 22 rf ranges, for all of $50 a year.
