I would strongly suggest that you find someone that has a 338 mag and shoot it a few times first. Shoot it with the bullet's you think you'd like to use. You have your bases pretty well covered and a 338 mag DOES recoil, I've owned two of them. You have all you need and then some for everything you want to hunt. If the "MAYBE" brown bear hunt ever comes off, you could then get a rifle just for that, or you could use your 300wsm. The recoil of the 338 mag can be managed, but not if you only shoot it once in awhile. You have only one cartridge that might have a bunch of recoil, your 300 wsm. Different people have different recoil tolerences, myself, I don't much care for it anymore. It is a great cartridge but big cases burning lot's of powder and fireing heavy bullet's have a price,,,,recoil!
I recently met a guy over in Prineville that bough a 375 just for an African hunt in 2008. He was told that the recoil is just a push. He say's his is murdering him, so much for just a push!