What's the weight difference between the gun he won and a possible 20ga? To me it doesnt seem like it would really be all that much and really not enough to justify buying a 20ga. Buying in for your girl is a good reason but I'd wait on that. For me it would come down to how much it costs to modify the 12ga...it really doesnt seem like it would be all that much to change out stocks...then later you can put the original one back on.
As far as recoil goes you can get some very lite 12ga loads that would kick the same or less than a standard 20ga load.
Not sure what kind of duck loads the 20ga shells typically come in but I know you can get 1oz 2 3/4" 12ga loads very easy. And you can find 1oz lead target/dove loads in 12ga very easy too...in fact you can find lighter loads as well if you go to a place like sportsmens or cabelas.