Well, never hunted coastal brown bears, but I have owned all those calibers and most of those makes of rifle, so I'll give my 2 cents.
My choice would be the Whitworth (Mark X mauser action?) in 375 H&H. Loaded with 300 grain Nosler PT's, or A-Frames, it will penetrate deep, and hit hard. The mauser action is about as reliable as it gets. Still shoots flat enough in case you get a 300 yard shot at a blacktail.
The 45/70 will be lacking if you get a long shot at a deer. The 338 and 35 Whelen will work, but since a big brown bear is over 1000 lbs., and probably going to be close, why not use the hardest hitting caliber of the bunch? If that 375 has a pretty wood stock, I would replace it with an inexpensive Hogue overmolded synthetic stock for the hunt, as there will likely be a lot of thick brush and rain every day.
Larry