[L]oading breaching rounds into a sawed-off double-barreled shotgun with a pistol grip seems counter-intuitive.
I dunno, that's more or less exactly the Knight's Armament Company Masterkey shotgun: it was essentially little more than a Remington 870 12-gauge pump-action shotgun mounted on an M16 assault rifle or M4 carbine as an underbarrel attachment. The M26 Modular Accessory Shotgun System (MASS) and Ciener Ultimate Over/Under system work on the same basic principle.
KAC's Masterkey only has a barrel length of about 7½" so it's not much bigger than the Remington Roomsweeper. I've always understood the Roomsweeper to basically be Max Rockatansky's sawn-off shotgun from the
Mad Max franchise, although he actually has a different "real world" gun as the basis for the prop in each film: a sawn-off VG Bentley in
Mad Max, another sawn-off VG Bentley in
The Road Warrior but with a different grip and trigger-guard, a sawn-off Rossi Overland 12-gauge in
Thunderdome (distinctive for its exposed hammers), and a a sawn-off Victor Sarasqueta 20-guage shotgun in
Fury Road. All four weapons are approximately the same size and you'd have to be a pretty big nerd to even realize they were different... You'd have to be a
massive nerd to track down the specific models.

The US military uses the M1030 breaching round, a 12-gauge 2¾" shell which uses a 40 gram projectile made of powdered steel, bound in wax. Typically fired at a range of 6" or less, although it will still do the job from 18-24" against most doors... It isn't meant to be fired at people, but it is absolutely lethal if fired at a human at such close ranges.