I have the same problems as you guys. 2 screws broken and stuck in there.
I had an identical problem with broken off head of the license plate screw.
So i drilled out the nut that is pressed on to the body and bought some rubber nuts and installed those instead.
Now, if the screws get stuck again i can just drill of the head, remove the whole rubber nut and replace with a new one with no problem.
Im thinking of doing this to the glass from the license plate light.
Just drill out a bigger hole for the rubber nut and install with new screw
PS! Its a little more work but sounds easy though.