Bladesmith, I just ran your formula against some guns in my stable. Here were the results:

Subject Gun Subject Load Weight of Ejecta (shot and wad, in pounds) Powder Weight (in pounds) Muzzle Velocity (feet per second) Gun Weight (in pounds) Fealt Recoil
J. Lang 12 Bore B&P F2 Subsound 7/8 ounce, 7.5 shot 0.0546875 0.01171875 1100 6.1875 22.1611455
Army Navy 28 Bore Blackpowder Load, 5/8 ounce, 7.5 shot 0.0390625 0.0078125 1100 7.4375 18.42095423
Perazzi MX-8 12 Bore Remington Handicap Load, 1-1/8 ounce, 7.5 shot, 4 dram eq. 0.075 0.015625 1235 8.875 45.80731919
Browning Citori 20 gauge Lightning Winchester AA 2-3/4" Trap loads, #8 shot, 7/8 ounce load, 2.5 dram eq. 0.0546875 0.009765625 1300 6.56 23.85369398

So putting it this way, an ultralight 12 bore London Best shooting 7/8 ounce 2.5" loads has less kick than a modern Citori 20 gauge shooting a modern load.

Interesting finding, huh?

Also of interest, a big bulky beast of a Perazzi trap gun still kicks 2x as hard as a London gun when the Perazzi is shooting a modern 1-1/8 ounce handicap load compared to the London gun shooting a 7/8 ounce vintage load.

Pretty remarkable, isn't it? A really heavy 12 bore still kicks 2x as much as a really light 12 bore? It goes to show that weight of the gun isn't a big factor in the formula, it really comes down to the huge difference between light loads and heavy loads. I doubt as many people would shoot 1-1/8 ounce loads over 7/8 ounce loads if they knew that it was putting about 2x as much wear and tear on their beloved double with each trigger pull.