Take a defensive or combat shotgun course, or at a minimum try patterning a 12-gauge with birdshot or buckshot in inside-the-house distances. You will likely find that you will be as comfortable with a 12-gauge as a carbine in taking a head shot in a hostage situation with buckshot or birdshot (my preference would be buck, but if not, #4 or #5 birdshot) at 20 feet. I took a self defense shotgun course from Texas Pistol Academy and was amazed at the tight patterns you get at short range, even with an open choke.
But serious training is a good idea regardless of the weapon you choose. We trained to do headshots in hostage situations, among other things. I am now quite comfortable with a regular stock, short-barreled Winchester 1300 with 4-ought buck for home defense.