A 12 round mag is not a "no no" unless you live in a state or municipality that prohibits high capacity magazines. I believe California prohibits any size detachable shotgun magazine. Someone correct me if I am wrong about that. Anyway, there is no federal law preventing you from having a detachable shotgun magazine of any capacity.
Back to the OP. Out of the box Saiga shotguns have 14 "countable" parts. As suggested, you can replace the magazine with an all US magazine (three parts) and either remove the barrel's thread protector or replace it with a US made muzzle brake (better solution)