Benelli Super Black Eagle 2: it's just designed well with an inertia driven system that doesn't use a gas system, so it don't have a gas tube that needs to be cleaned out. It also takes strong magnum loads.
Benelli M4: it's reliable enough to pass U.S. Marine corps trials, and has an adjustable stock, a feature not found on most tube fed shotguns.
Fostech Origin 12: it's a semi-automatic shotgun that takes detachable magazines, enabling fast reloads. But I reccomend getting shotguns fed by fixed tubular magazines beforehand becuase of how hard it would be to find the magazines for the Origin 12.
Winchester Super X3: can have its magazine capacity extended up to 11 rounds.
Manual action shotguns:
Benelli Supernova: it's a pump action shotgun with a solid mechanism and can take magnum length shells.
KelTec KSG: it's a pump-action shotgun in bullpup configuration. It is very compact, but holds 12 to 14 rounds of ammunition, depending on the length of shells it's loaded with.
Mossberg 500: it's an easily customizable pump-action shotgun that can be installed with a metal trigger group and a variant, the 590/590A1 is used by the U.S. military. Similar goes for the Remington 870.
Paradus LAX 12: it's a lever-action shotgun that can hold up to 5 rounds in the magazine, plus one in the chamber and another one on the loader. It's Category A in Australia.
Manual-action and pseudo semi-automatic rifles:
Barrett Model 95 and Desert Tech HTI: both can fire .50 BMG and are magazine fed bullpups, with the former also being able to take smaller rounds.
Southern Gun Company .223 lever release rifle, and
VZ-58 MARS; they can simply be quickly fired.
Henry Octagon: it's pump action and can feed loose rounds without a proprietary magazine, instead using a tubular style.
Browning T-bolt: it's magazine fed and quick to fire.
Ruger American Rimfire: can use high-capacity 10/22 magazines.
Non-restricted carbines (Henry Mare's leg, BRS-99, Chiappa 1887 T-series):
all of these would work great as non-restricted pistol substitutes. I think it's possible to get a holster for the Henry Mare's leg (which can serve as a great backup hunting gun), and I can imagine a custom or 3D printed specialised holster for the BRS-99.
Note about .22-250 Remington:
AE22250G has more range, but the P22250G is more powerful;
Remember that .22-250 Remington is originally developed as a civilian hunting round, and P22250G was developed more for shooting medium sized game while AE22250G was developed as a varminting and target round. So just keep in mind that you're essentially taking a hunting and sporting round with hunting loads and pressing it into either a self defense or, much less likely, paramilitary (ie prepper group, maybe security-patrol) purpose.