If the 12 is heavily built - it will work just fine, especially with smokeless loads.

The heavy 2 3/4" load IIRC, was 7 drams - 191gr. of black powder. This produced some 1,500fps to 1,550fps with a 12 bore ball of some 583gr. weight (1.33ounce) in pure lead or hardened at about 554gr. weight - 1.25ounce approx.

You can do this with smokeless powder with about 50% the recoil - the BP load is not fun to shoot, for me at least. You might like it, but it was hard on my stock - split down the wrist and needed repair. After that, I used only smokeless.

The 10 bore AYA I used lead in for geese - many years ago, was built much more strongly than any 12 bore double I've had. Shortened, it would weigh about 9 pounds and would also shoot a heavier ball, but with gas check cups to hold the ball centered, it could shoot a 600gr. .735" ball easily in it's .774" bore at much higher speeds & more easily than a 12 bore would do with a 12 or 13 bore ball.
With the undersized and smaller ball you should be able to achieve 2,000fps or close to that with that 600gr. ball - that's bear smackin' power!

Ed Huble might be able to suggest where to start with loads. They might already be in his thread - for suggested places to start, that is.

The gun's extra weight would also help, but know that 3 1/2" cases would probably be used and they would take a lot of wads to fill, which increases the ejecta and therefore recoil for any load. 2 7/8" might be better, however are they available new in plastic or perhaps paper?