" The reason I ask is, I've wanted to hunt brown bear up there, but was told by an experienced hunter who's hunted Alaska several times (and taken Grizzlies) that the 300 H&H is "not enough" for the big bruins, especially from a single shot (Ruger #1). He seemed to feel that a bear hunt using my single-shot was too risky, even if backed-up by a PH with a 416 or 458WM."

Nick,
When I lived in Alaska one of the most popular rounds was the tried & true .30/06. There was a story in one of the outdoor magazines about a guy using one to kill a polar bear that ate a native. If it is good enough to use on bears the .300's are even better. Just remember the two main points. #1. quality bullet (Nosler PT or my favorite the Barnes X for suggestions) #2. placed in the right spot. If you do these 2 why wouldn't a Ruger #1 be perfectly fine. Some people might say you can't always put the bullet in the right spot and have to take what shot you can get. If you can't put it in the right spot DON'T TAKE THE SHOT.

I hunt with a .300 H&H and it has never let me down. The only draw back for some people is that it is a handloading only proposition unless you want to spend some major bucks for ammo. I am a handloader so it is no problem for me.