I bought my original edition .444 from a friend who carried it in Alaska for bear protection while working as an engineer on sawmills. He never had to fire it, but felt confident. Everyone carried a .45-70 or .444 as they walked through the woods, and one of his co-workers killed very large belligerant black bear at close range with one shot that entered the neck, broke the shoulder and spine, and exited at the backstrap in front of the hip.

Beretta, Merkel, Kreighoff and others offer the .444 in O/U double rifles for stalking wild boar, which run 400 to 500 lbs in Europe, and are more dangerous than most black bears.

The Hornady 265-gr and Speer 270-gr are great bullets.
I would like to try the Barnes 300 gr at 2100 fps.
That, or one of the hard cast 300 to 325 grain bullets should work. Go to Buffalo Bore's website and read their 3-part article.