That looks like a muzzleloader. Just because you can put a quarter pound of shot down the barrel doesn't mean you have to. Most people who shoot 4 gauges put in only enough shot to fill the sky.
I hardly ever put more than 1 1/4 ounce of shot in my muzzleloading 8 gauge except for that time that my brother wanted the "full 8 gauge experience", once was enough.
BTW, that gun throws excellent patterns with 1 1/4 ounce loads.
I have made three 4 bore rifles and four 4 gauge shotguns. With a service load, the recoil is a bit brisk. In fact, it's so brisk I won't zero in the rifles any more. I leave that to the customers. Here's a picture of a man shooting one I made. It's loaded with only 350 grains of powder in this photo. The service load is 425 grains. A “magnum load” is 600 grains, but no one was willing to try that, least of all me.This man is 5' 9" tall and weighs 175 pounds.
You'd done have to be a rocket scientist to figure this physics problem out.
Yikes, that's 350-gr load, a 600-gr load would have a significantly brisker recoil. I'm guessing a 4-ga gun would go a long way in helping you develop a flinch! When I was young and crazy, I shot a .460 WebMag in a light safari rifle, once.
I want one for each hand!! In iowa anything over a 1in bore is illegal I don't think there is anyway around that in iowa. We can't have suppressed, auto or short barreled either. Silly laws punish the ones who use them in criminal behavior not the ones who don't.