The list of single shot rifles is LONG. Marble (as is Ax and sights) used to make a "game getter" that was a rimfire barrel over a centerfire barrel/ .22 over .44/40 I think my uncle's was he said... Great for collecting specimens. You could shoot .410 shotshells in the .44 barrel. It was outlawed when rifle barrels had to be 18 inches (really fights crime), later changed to 16 inches. Still 18 for shotguns. Minimum.
eabco.com has a custom rifle you could set up this way.
Fed law, rifle barrel has to be 16 inches long generally. I think the pistol gripped shotguns were a "destructive device" at one time and needed a $5.00 tax stamp. And there are some recoil reducers that would get you to 20 inches if you must.
b) In US, 2nd Amendment, guarantees gun ownership, so they suppress suppressors. There are lists of class 3 dealers and Shotgun news often has advertisements. Some magazines. Look for dealers in "full auto." As you indicate, this is a tightly federally regulated firearm. My favorite FFL told me that silver solder was a permanent attachment for the law. Lead solder was NOT. Ironically, outside US where guns are much regulated about anyone can buy a silencer/suppressor. Now getting something to put it on??? So if you are near a border...
State laws govern hunting mostly. There are federal migratory animal laws. Yes, check locally for option to hunt.
From there, about any single shot would do. T/C has the "big dog" in this field right now. Many custom barrel makers speak of restricted barrels for law enforcement. Usually mean silenced or suppressed. Just have to shop. From there it is about any single shot. Winchester 1885 or Browning copies. Hiwall or low wall. Ballard did a gun now copied. The ungainly sharps. Numerous other falling block copies. Seldom cheap. MOA had a pistol. No idea if they ever got the buttstock offered. In the back of Gun Digests there are lists of currently produced firearms. I would start there and go with what looks go and I can afford (ha, ha). luck