Bummer. That's the exact reason I shy away from screw extractors. Once they snap off, they're VERY difficult to get out.
It's a tedious process, but I've had success on really stubborn broken screws by drilling as close to center as possible, then drilling with successively larger bits and when the screw shell gets thin enough, using a sharpened punch to collapse and remove the screw. If the original threads get screwed up then I break out the helicoil (or go buy a set if I don't have the size).
Hope you have better luck.
