Strengthening a door panel?

The vehicle is a 93 grand marquis, so after 17 years and 90,000 miles of slamming the doors the inside trim/panels (all one piece) has developed some flex and noises. All of the clips are strong and the panel fits tight around the edges however if you look at the center of the panel while you shut the door there is quite a bit of flex. I really want to fix this but not sure how to go about it. I thought about screwing it down at different points but I dont want them to show and there really isnt a good place for the screws. I thought about reinforcing the back of the panel but not quite sure how I would do that. If anyone has experienced this issue (with any car) and found a decent way to cure it please feel free to chime in. Keeping everything to appear stock is a must, the interior is flawless except for this.