Mentokk1,
I've got a Winchester Ranger 120, which I believe was between the 1200 and 1300. I use a 1300 slug barrel on it (but it was a 3" gun). Badger Barrels used to make slug barrels for all the shotguns. They restructured a couple years ago, but the guy who owned it was very sharp on the dimensioning and differences between various actions. Might call and see if you can get help there.
I think the rotary bolt has enough lug bearing area to handle rearward bolt thrust, which is where actions have to be strong enough. Look at Lilja's barrel page for the calculations on this. The barrel's made for 3" so it'll handle the hoop stress of the 3" shell. I think I'd worry about whether the elevator will reliably feed the shells from the tube magazine (or if they'll get stuck). Also, whether the bolt pulls back far enough to let the fired shell eject, even if you cut the window 1/4" wider. You might try cycling the longer shell (with the barrel off). You also might pop a 3" empty onto the bolt face, retract it, and see where it leaves the front edge WRT to forward edge of the ejection port.
But I'd also ask Badger Barrels if you decide you'd like to do it. Or might call Hastings.
HTH,
Steve