To answer some of the questions directed at me, I don't know if CZ will make a 404, they should...I think the 404 is way better for Alaskan bear than the 9.3x64..

I have used the 416 Rem for years or since its introduction and never had a pressure problem with it, if one does it because they put too much powder in it

I cannot tell any difference in killing power between the 416 and 404, and I would even toss in the 458 Win. with a hot handload in that ball park...

If the first shot is correct and bullet construction is correct, then one caliber is about as good as another IMO, and a charge is best stopped with a bullet in the brain and the size of that hole has little to do with anything.

But I will allow that one should shoot the biggest gun that he can shoot easily under adverse conditions, bent over, squatting and prone is a good test, if you dread pulling the trigger you need a smaller caliber...