Over fifty years ago, Elmer Keith & company developed the 334OKH. Elmer later stated that, with very minor changes, it was similar to the 340 Weatherby. Elmer also said it was the finest long range big game cartridge ever. Forward 50 years, the manufacturers & publicists tout the 338 Lapua - just another version of the 340 Weatherby and Elmer's 334OKH.Don't overlook the 340 Weatherby. There is high quality factory ammo, and reloading components and dies. Pick a Mark V with a 26" or better barrel and a muzzle break. Accuracy will be a concern: 1 moa is about 10" at 1000 yards, and it's much harder to mantain at 1000 than at 100. A good scope is needed. If you aren't carrying it, I suppose you aren't still hunting, so a 3 or 4 power low end on the scope is likely OK. I like Swarovski.
The 340 Wby has been sitting around for years without much attention. It's equivalent to a 338 Lapua. It's recoil is a little bigger than the 300 Weatherby (or 300 WinMag in a lighter rifle). It's way more than a 338 WinMag. Get enough eye relief.
My stainless synthetic Rem 700 in 340 Wby sports a 25" Douglas Premium barrel for ease of hunting use and has been used all over the US, especially Alaska. It shoots 250gr NPs into 2-3/8" at 300 yards. Needless to say, I'd carry it anywhere.
However, unless the OP plans to hunt in the vicinity of big bears, a 26" barreled rifle in 7mm Rem Mag would fulfill his stated needs very well without the extra costs and recoil of the larger cartridges.