Quoted from PinBallMagician:Have you tried putting foam against the back?
This is probably the best suggestion.
The other suggestion is to lessen the power to the flippers. The easy way to do this is to add extra padding to the end of swing (that's the wrong term) stop bumper in the flipper assembly.
As for padding at the LW3 hole, you can probably find some thin padding at the craft store that would work. You won't need much.