Well, you can't hunt Canada with a handgun, and you can't hunt grizzlies in Alaska without a GUIDE.....

So your problem is solved, if you want to hunt grizzly/brown bears with a handgun...

Don't hunt in Canada...

Use your .44 in AK..You'll have a guide behind you with suitable stopping rifle, so you can leave your rifle home...

Have a ball hunting black bears with your .44 in the lower 48...No place there to legally shoot grizzlies..