What is the definition of "shotgun" that CA uses? If it is this one then you may be onto something:
A firearm intended to fire from the shoulder
that uses a shotgun shell to propel one or more projectiles through a long barrel with a smooth bore. It may have one or more barrels. "
I don't know if the Saiga-12 uses a standard AK flat, but if so, this might work: buy a demilled Saiga-12 kit, build one up from a flat with 18"+ barrel, AOW it with a 16.1" barrel, dual pistol grips, and have it take a detachable magazine.