The issues you will run into are 1. shotgun firing pins are too big and blunt and not very well sealed to the breech; 2. shotgun actions are not designed to take anything but the tamest calibers (hence popularity of the 45-70); and 3. putting inserts down the bbls is a short cut but it leads to a rifle that feels like it has two lead pipes out there.
If you want to do it within the design envelope of action, then build a paradox or a bore-rifle. A 12 is the standard, a 16 is more interesting, and a 20 is downright sexy. Paradox requires only rifling the (full) chokes, sights and reregulation; bore rifle requires sleeving, sights, and reregulation.
Or I will sell you a FinnClassic 512S (formerly Valmet 412S) with a set of 9.3x74R bbls that you can regulate to any load, with an extra set of screw choke 12 ga bbls, for about what you gunsmith is going to bill you to do the above conversion; and you can scratch your itch next week.