Look, for a handgun, 44 mag is as good as it gets.
Unless, you go
45-70 in this . . .
I hunt deer and turkey up near Colville WA right in your area and have never seen a Grizzly. And I've hiked in deep through private land right up to the Canadian border with a couple of hunting parties. We've heard the bellows of a moose once, seen moose scrapings on trees and seen moose scat several times. They are around.
Most likely, mountain lions and cougars are the dangerous game you'll run into other than a horny pissed off gobbler who can't raise a harem during the Spring.
To be safe, buy your Dillon 550 press.
Buy some new Starline 44 mag cases, a max load of 19.0 grains of Hodgdon's H110, some magnum primers, some 300 grain Laser Cast truncated cone hard cast lead bullets and you can do 1400 fps. Giving you a good 1,200 + fpe and plenty of penetration to break bones and damage vital organs.
And try to run uphill as you shoot. use their weight against them. Downhill and they roll over on top of you.
You've got to reload for 44 mag anyway unless you'd like to pay $540 retail box by box for a case at your local gun range ($25/box plus 8% tax).
You'll never shoot it well enough unless you do!
Carry your 44 mag.
And tie some bells onto your clothes and call Dept of Wildlife and ask locals about any "animal" sightings and you should be fine.
And a friend with a 45-70 guide rifle would be nice too.