You may already know this. 1891-1939 crown over S, supplementary mark designating shotgun barrels, crown over W, supplementary mark indicating barrels with choke. The two eagles (if that is what they are) provisional and definitive proof of shoulder arms. At the far right is a circle that should contain a number indicating the gauge. The proof load varied depending on chamber length.
I agree that the large crowns have to be a makers mark or perhaps as Jerry suggested a type of tax. Also, if the gun was made after WWI there was a limit on the arms production, so they may have something to do with that.
Pete