Obviously, you guys misunderstood me. I'm not talking about drilling into the motor mount. I'm talking about using a drill bit to grind the head of the screw off. If you use a bit larger than the shaft of the screw, when you get to a point, the head of the screw will fall off. If you don't drill too far, then you will be able to grab the shaft of the screw and twist it out.
If you are careful, you won't ruin anything other than the already wrecked screw.
Maybe you doubt it will work, but I've used that method many times. I am quite a ways away from a lhs, so I re-use my screws until I destroy them.