Failing the removal of the screws, I'd grind them flat/smooth/flush with the hinge's surface, re-drill new 1/4" holes, with a countersink (using a drill for metal), and install two (2) new flat-head screws to match those of existing. Re-drill the new holes about 1/2" away from the existing abandoned broken screws.
If it were me, I'd drill the screws out with a bit somewhat smaller than the screws. Once you get them drilled out some, I'd try a screw extractor. Once you get them out, stuff the original holes with glue and toothpicks (or wood skewers), if the holes get buggered up, and then put in new screws with better specs than the originals.
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