First, I think what everyone has said needs attention first. However, if you have access the the underside of the deck, you could add some glass and a piece of 1/2" wood around that area to help stiffen it up. I think this would help a little, but as long as the hinge is over rotating, you will still have the problem. Possibly a good place for a custom sticker? I know that would be covering it up, but it is really just a cosmetic thing and unless it over rotates to the point where it tears the glass, then keep on keeping on.
What about one of those rubber little round pads like those that are on kitchen cabinets to keep them from slamming to help prevent any gouging? Just a thought.