I offered to do a screw extraction on someone's pistol one day. Of course Mr 'been there done that' sidled over to tell us it never worked, complete waste of time trying really.

After much heaving out it came, sweet as a nut

I have two secrets for success...

1: A modern woodscrew on the end. The kind with a really sharp point and razor sharp, narrow flutes.

2: Have a bore sized plug behind it so it has to go though the ball centre, not between ball and barrel.