I have had great success just putting some thick tape on the playfield for protection, then drilling a very small (1/16) hole in the center of the broke off screw, then use a hand turned drive (not powered) screw extractor that is just a tad bit bigger than your 1/16. It will grab and get the screw up above the playfield just enough to then either 1.dremel a slot in it to remove it with a small straight screwdriver OR, place tiny vice grips on it and turn it out the rest of the way. I've used this method many times without failure for 10+ years. It is time consuming but if successful, you can never tell anything was ever wrong with that screw/post.