Fridge top screw for stationary arm

[tranquil]

Greetings

On the right side of the fridge top is a silver metal adjusting "arm" that can be rigid to hold the fridge top upright, or flexed to fold down when the fridge top is closed. The top bracket of the arm has 2 screws that attaches to the fridge top, which has broken through. I've attempted to glue a small piece of wood over the hole and re-screw; have attempted to adhere with 4200, but nothing holds. Assume this is because the top is hollow with just a thin layer of material on the side that goes into the fridge where the screw/arm is attached. After a few times opening/closing the top it breaks out again. Don't think there is space to move the arm over at both ends and re-attach without obscuring quite a bit of the opening, but maybe?---has this occurred for anyone else and any ideas on how to repair?

Thanks
Teri