I've had or do have all those you mentioned with the exception of the .404. That's not to say that I haven't seriously considered grabbing a .404. It's really a .423 and can be loaded up to surpass its traditional ballistics. It doesn't have the sectional density that the 416 does.

That aside, I'd get them all if I were you...

But, if you have to pick one, I'd go with a 416 remington or rigby. 400 graines at 2350 is plenty for any coastal grizz, and it's slow enough that it really isn't a problem to use on smaller critters (with regards to meat damage). You can always hand load it with a 350 grain bullet. I've shot white tail, and many o pig, with it, and it's never been an issue. Recoil, for me, is not so terrible.

The 375 H&H will probably be the most popular choice among those posting their opinions, but I think the 416 makes more sense. It really nearly shoots as flat as a 300 grain 375 H&H while delivering a lot more energy and penetration. If you go with the remington instead of the rigby, you won't have problems finding ammo either.

If it weren't for the grizz issue, I'd tell you to go with the 338 win mag. It certainly does have the power to kill any bear with a well placed shot, but if you bump into a bear in the thick stuff, you'll want that 5,000 lbs of energy behind your frantically shot bullet. It shoots flatter than the 375, has almost as much energy down range as the 375 H&H, and has a good variety of bullet weights with which you could choose.

All that being said, the smart choice might be the 375 H&H, as it is a great round. However, if you can handle the recoil of the 416, go with it. It'll do anything the 375H&H will with more juice, and out 250 yards, the difference in drop is only a couple of inches.