If you are looking at like a Ithaca/Holland Arms Auto & Burglar style, it will most likely have to be custom made. TMK, never saw an aftermarket PG for any double, just for NEF singles. Probably due to unwitting SBS violation. Plus, usually stock blanks usually come in some kind of profile. It's possible a custom stockmaker would just be attaching a wood pistol grip under the tang ala the M1 Carbine Enforcer or the one Ramline (and Ruger on the FS model) made for the Mini 14. Iy would look like crap with checkering left on the original wood, possibly structurally weaker. Otherwise you're talking real money, constructing a wood PG handle from scratch.
True sawed-off, coach guns had a whipit stock, something there, that goes back to the Blunderbuss age. Probably often too short to function as a real buttstock, but something there, like a counterbalance. Just get your crosscut and some sandpaper, masking tape make sure to keep the whole thing over 26" (check local laws, here in MI going under 30" would make you guilty of an unregistered handgun if you don't) and that's before adding a pad if you do. And make sure not to cut into the stock bolt. It can be a half stock or a hogleg style knobby PG (where you really gotta watch the stock screw and maybe have to shorten or replace anyway)*, but DIY is what you want to do.
Do the work on a second stock if possible, buy another.
I love compact long guns, personally think the SCG is handy enough. Any grip angle alteration too with impede use of controls, the safety and opener were designed to work with your hand in a different position

this is not the real A&B style butt, which was square backed and a 90 degree L shape. This is a hogleg style. Your 20" pipes and this: 26.5"? Hope you have the black stock, or it will never look good. This way would allow access to controls though.