You already have a .30 cal rifle that shoots amazing.....
All you need now is something to fill that gaps. I would suggest a .243 for the predator/pig hunting that is pretty darn good hunting in your current backyard.
For AK build yourself a 338 in the 10lbs area like stated prior. My current one weighs at 10lbs topped with a nightforce 2.5-10x30 scope, loaded, sling, stock pack, and bipod. I finally had a chance to shoot it at 600yds and it prints good on paper. I am only shooting 225gr accubond in it but may step up to the 250gr for next season.
I don't know how the 300gr matchkings will do on the brown bear at close range so I might have to carry two different bullets with me. Nosler partitions for 200yds and in and some 300gr matchkings for the longer shots on everything else up here.
Of course you need to start reloading or make friends with someone down there that does and just bring your dies and components. Besides that you need to remember the lead time on getting a custom rifle
built. Get your order in so it will be waiting for you when you get back from your next "hunting" trip.