I'll give the same response I always give on lefty questions like this - remember there are rifles out there that work just fine without a bolt handle. My choice is the Ruger #1. My first "bigger than an '06" rifle was a #1B in .338 Win. Mag. A friend wanted it bad so I sold it. If was a little bulky for me in the hand anyway. My latest is a #1 Tropical in .375 H&H. Either work perfectly for lefties and I love that tang safety.
Another lefty option that looks interesting is the .338 Marlin lever action. My elk experience is limited, but even here in AZ most of the shots I've encountered have been less than 100 yards. The printed ballistics of that Marlin round should work just fine at 3 times that distance. I only wonder if the cartridge will have longevity...
