Honestly probably not any farther than a 2 3/4 load of buckshot in a standard 3 inch barrel. And it would kick a WHOLE lot less would be my guess.
As with any other gun your max rang is really going to depend on what your gun does with a particular ammo and how well you shoot it. Yes effeciency of the load is a factor, but it doesn't matter how far a load will work if you can't hit anything with it

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Buckshot is made for close up kind of work, not longer distance stuff, that is what slugs are for. I would say keep it in the 40 yard range if your gun patterns well enough for that. I would be looking for tight patterns at that distance, like enough to keep the shot in the vitals.
With buckshot you need to pattern your gun just like you would with any other load for any other game. Even more so in my opinion. Don't be afraid to try different chokes and different loads. Even 2 3/4 and 3 inch loads, your gun should shoot them just as well. Just because you have a 3 1/2 inch gun doesn't mean you have to shoot those big ole shells out of it.
My buddy has a 3 1/2 870 special purpose turkey gun and it shoots anything you put in it, I would assume yours is the same. He also has a rifled barrel for it. Anything that will fit an 870 will fit your gun, you don't need a special barrel if you get a different one. He just went out and bought a standard rifled cantilever barrel from remington. Shoots absolutely great.
I personally don't care for buckshot, but I supose it has it's purposes and it is legal so I try not to bag on people that use it. If I wanted to shoot that close I would just use my bow or maybe get a handgun. In my opinion though if you want to shoot farther than 30-40 yards you should see how some rifled slugs shoot out of it, or get a rifled deer barrel which will extend your range quite a bit farther.
Good luck,
Paul