Current thinking seems to be that a flat-nose .44-45 caliber bullet at ~900 fps will penetrate a deer completely. I no longer hunt, so it's all academic.

I will say that I've shot all my old .44 Mag full-power ammo, and the brass will be reloaded with enough BE-86 to send a 240-grain LSWC ~950 fps from my Old Model Super Blackhawk.
John Taffin was fond of saying that a 250 grain bullet at 950 fps from a 45 Colt would penetrate a deer north to south. Tim Sundles at Buffalo Bore says about the same.
I load my Ruger Bisley 45 with the XTP bullet to 1,200 fps but have not killed with it. It easily shoots 2 inch off hand groups at 25 yards and being manageable I have not tried to increase the speed. My plinking load for that gun (45) is a 200 grain FP Berrys at 1,150 fps, about 600 fpe.
I try to run the 44s and 45s about the same weight and speed, no downside I have noticed.
On the 44 special, I do not have a Charter Arms and I understand why people load them so lightly. My smallest is a 30 ounces snub in 44 mag. I do like the 9.0 grains of Unique, they are thump enough for any defense use, people, hogs, dogs, or black bear, yet not abusive.
As I have aged, (76), I have lost interest in being macho and shooting 100 rounds of hot loads at a sitting, so I shoot lots of 22s and concentrate on precision with however many of the 44s or 45s that I choose to shoot on that day. If I fire 5 groups of 5 and they are all tight groups, sometimes I just pull that target and stop right there. As an instructor for many years, I know that shooting longer times does not improve accuracy or speed, just burns more ammo. Just something that I do. I have been that guy that took boxes of top end 44 mag to the range and shot all of them, but maybe 6 from the last box to leave in the gun. That sounds silly to me now.