Couple of thoughts. I built a "hybrid" stocked/whippet. Once I got the stamp back, I sent the barrel to Steve Rose and had it cut to 2 inches past the mag tube cap. Added a Nordic +1 to even it up and add a QD cup. As others have mentioned, the action spring and assembly don't allow for a pistol grip or even normal sized birds head grip. I personally don't know of a semi-auto shotgun that would work for that. Maybe something elongated, but I didnt go that route. Instead I cut the stock down by about 3.5-4 inches and mounted a grind to fit pachmayr pad. I was wanting the idea of a short handy semi auto that could be shouldered vs shot from the hip. Keep in mind, the A5 and its cousins use the brass friction rings to adjust to different loads. Shooting from the hip/wrist can be brutal if there is a mismatch between friction ring orientation and the load.
I had enough parts left over (barrel, newer trigger group, bolt, etc) that I decided to try the OP's idea, and did buy a Sarco receiver to start a second build. I can't speak to whether it is "virgin" for the stated purpose (I'm thinking mock Rhodesian for this one) but it was a good buy. Had to clean up some rust with a wire brush but it is in great shape otherwise. Be prepared though, Sarco is a grumpy pain in the ass to deal with. But as others have noted, getting the rest of the parts from a supplier would nickel and dime the project to a costly death. I'm gonna table the idea until I can find a cheapy gunshow donor.