I have no doubt about your skills or ability to shoot George. Nor do I doubt that with the right shot a 44 mag will kill a grizzly, I did and so have other folks. The problems comes if you don't happen to hit it just right, then what happens.
Old griz is faster than a race horse for short distances and a frontal charge does not leave you with much to shoot at. Unless you short circuit it's brain or spinal cord or break some big bones that allow it locomotion you may have a hard time stopping it. If it's charging you it's probably also not to happy.
Of the several big bears I shot in Alaska I always preferred a side shot where I could break the front shoulders. Remove the means of locomotion and there's time for another killing shot. I used both a 375 H&H mag pushing well built 270 grain bullet or my 8mm Rem mag pushing well constructed 220 grain bullets. I always used a follow up shot even if I did not need it on a brown bear. Of the few grizzly/brown kills I made all were without incident, but I've been on a couple of hunts with other folks that really could have turned out nasty.
I went with a new Captain assigned to our unit one year. We found a nice bear down in a small hollow about 75 yards from us and from up on the ridge where we were watching he appeared not to see us. I told my friend to just sit and wait til the bear turned sideways and do a front shoulder shot with his nice new 375. I don't know if he winded us or what, but the bear stood up facing straight on toward us and the next thing I hear is that 375 going off.
The bear went down like it was pol axed. He says lets go down and get it. I says lets just sit here for a while. The bear wakes up about 20 minutes later. He had hit it right on the forehead at a shallow angle and took a six inch diameter patch of hide and fur off the top of it's skull. It wasn't dead and it certainly wasn't happy when it woke up.
I never seen such a mad animal in my life. It was squealing and tearing up the ground and running around in circles biting at the brush and it's self and ripping whole patches of brush out of the ground. When it stopped for a moment I and my friend broke the front shoulders with my 8mag and his 375. End of Mr. bear, but I put another round it for good measure.
It tore up the ground where it woke up in a 30 foot circle including pulling out 10 foot high clumps of brush with three foot roots attached. It looked like the ground had been roto-tilled.
There's lots of incidents where folks armed with a variety of rifles and handguns have had grizzly/brown bear encounters and were unable to stop a charging bear. Yes try with whatever you have handy, I would because the alternative is not something any of us want to contemplate and some simply don't live thru. I can guarantee that if you do make a good shot and stop the bear it can be a life changing happening.
Just keep in mind that these are big animals armed with sharp claws and teeth and though not bullet proof there are plenty of documented incidents of folks that were crack shots of steadfast courage are now growing a rock in a grassy place with a born and died date on that rock.
This is one case where we are not at the top of the food chain and a bigger gun along with the ability to shoot it well sure seems to be good insurance to me.
Bob from Idaho