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Your only other possibilities may be to grind the heads off with a high speed grinder or to begin chiseling them off. You may be able to use a Sawzall type saw to saw right through the hinge and screw. These will allow the shank of the screws to remain in the door, but the hinges will come off and you can make a small adjustment in the new hinges for new screw locations.
I know the extractors are for broken screws and bolts, but the principle is the same.
I know from experience that all of the methods I have mentioned work to accomplish the task. At times it just takes more effort to do the most simple things.
Get a center punch and a light hammer. I
wish I could draw you a picture, but....
Pick a point in the cam-out part of the slot
in the head that's near the edge, but still
has some room for the punch to dig in. You're going to be tapping gently on the
punch, but not perpendicular to the door.
You need to lean it over so that the tapping
will tend to move the screw counter clockwise. For instance, if your punch point
is at the twelve o'clock position, you'd lean
it to the right.
Tap a little, then pick another point on the
opposite side of the screw head, and tap
there. Go back and forth between the two,
and see if you can get it to move. Silikroil
or WD-40 may help.
This is just one last thing to try before
renting a grinder or calling the locksmith.