James, your thinking too much
First of all, what's the serial number??? Second, Parker didn't make actions according to gauge, they made them to the frame size (distance between firing pin holes.) If your sure it's a #2 frame size, it could be anything from a 10,11,or 12 gauge in that time period.
Or are you saying the receiver's (you call it the action) serial number is different than the barrel and forend serial numbers???