I would try lightly kicking him in the nose with my toe when he has his head all the way to the ground. Not a kick that will hurt him, but just enough that he'll feel it and move his head up to get away from whatever "stung" him in the choppers.
Don't get into a tug of war with him by trying to pull his head up.
The shoves are very disrespectful and should be reprimanded hard and fast. The instant he shoves you with his head, step toward him and send him backwards. Make it seem like the whole world just came crashing down on him. It will be a little tricky because you won't have anything on his head to help control where he goes. If you work with the Parelli 7 games, this is a great spot to do the YoYo game (which can be done with a rope halter tied loosely around his neck attached to a lead rope).