Why don't you wear the saree as it is and use a seperate dupatta to cover your head? I have seen almost every bride do that in Hindu weddings and it looks nice. Of course don't use some plain or cotton dupatta, use a nice embellished one that goes with the saree.
it does look really nice and my hindu friends get a net dupatta with a heavy border because it's super easy to keep a light dupatta on your head and the net material is very easy to stay in place.