Another option, once a small center hole is established, is to use a very small diameter diamond dust burr in a Dremel tool, and carefully remove the screw stub a little at a time out to the minor diameter of the thread. Then use a bottoming tap with the same diameter and pitch as the other screw to restore the original threads.
Jerry

"It is better to be silent and be thought a fool than to speak and eliminate all doubt!" - Abraham Lincoln
Cringe and wail in fear, Eloi- - - - -we Morlocks are on the hunt!
There is nothing noble in being superior to your fellow man; true nobility is being superior to your former self. - Ernest Hemingway
Love your enemies and drive 'em nuts!