I guess the first question is what is a 3-3/4" barrel on a ,44 mag good for? Flame, fire and no better then a .44 special +P. Recoil will increase to .500 levels.
I had a funny thing happen when shooting my BFR .475. 7-1/2". At 50 last week I had shots touching and adjusted to center. I found they were Lee 400 gr bullets. NOT mine. I found mine and shot this morning today the first shots touching and 2 clicks down got center. Many large calibers need 5-1/2" to 6" at least but I want at least 7-12". A real short barrel is a one shot at a bear since the gun will be 90 degrees up so you will never get another while the bear has your head in teeth.
I guess that velocity depends on the load. If you google short barrel 44 mag loads, probably 100 FPS compared to a 5 1/2 barrel. Seems like plenty of loads to get a 250 grain slug to 1250 fps, and for my area that will flop anything. Bears over 300 are pretty rare, and deer over 150 just as sparse.
I also carry a SW 329 PD lightweight pistol and it has a 2.5 inch barrel, same as the Ruger Redhawk Alaskan.
I saw a video on the same 3 3/4 Blackhawk where the Buffalo Bore 340 grain bullet (340 not 240) was going an average of 1231 FPS on the guys chronograph. 1140 FPE is enough to make it through the slats of a PA whitetail. A tad better than a 44 special.
https://www.youtube.com/watch?v=xumQoyyIiLMNot so much the loss of power. 3 things happen though, first spin of the bullet is reduced, short guns are harder to aim and recoil goes way up.
I think spin is the most important for stability so ranges are shortened. 1/2 gr of powder can change things from a tiny group to center of elephant. I still think as barrels get short, twist should speed up. The DE has 1 in 18" and the BFR .44 has 1 in 16". Ruger is 1 in 20".
My old IHMSA SBH has a 10-1/2" barrel and I use my 330 gr bullet that needs 1316 FPS. I tried Unique to around 1100 FPS to get about 2' patterns. You can't burn a full load of 296/H110 in a short barrel.
Sorry I am not catching some of your points. Spin is due to twist, not barrel length. I don't think length has anything to do with stability given appropriate bullet hardness and rifling depth. In fact a slower bullet from a shorter barrel should need less twist. For example. a 1/60 twist is dandy in a 62 caliber flintlock with a 325 grain ball. In a typical flintlock barrel of 30-40 inches or so, the bullet does not make one complete spin. I think most would go to a 1/72 twist at 62 caliber, than 1/48. Anyway weight and hardness of the bullet are integral in the stability equation. Anyway for a 240 grain slug a 1/20 is dandy in any length.
Shorter guns may be easier to hold due to balance, so saying longer barrels are easy to hold is subjective. In some cases like match 22 rifles, shorter barrels reduce dwell time reducing the need for follow though. That is why they make sight extensions and keep barrel short. A person could also claim the weight of a BRF in any length is harder to hold, but again that is subjective. I know my wife can't hold a heavy pistol, but does better with lighter models.
Recoil is hard to define, but as the barrel gets shorter (with the same load) the bullet energy goes down. I think you stated the loss of power and said the level was 44 special-ish. So recoil should also be reduced proportionally. Of course shorter barrels usually mean less mass, so that is part of the real perception. Moment arm leverage is more for a longer barrel, so that causes more flip, but more mass helps dampen the flip. Lighter pistols kick more due to mass, and grip design has a lot to do with perceived recoil. With my paws, I feel less recoil in a Bisley than a plow handle. That is why I bought the 3 3/4 SBH, it came is a Bisley grip. I would have liked the 4.5/8 barrel better, that is why I just bought the 44 special 4 5/8 in a Bisley.
