Get a Dremel* with a thin cutting tool and cut slots in the heads of the bolts. Then use a flat ended screwdriver (impact if possible) to undo the bolts. Replace bolts.
@Brommers started
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Get a Dremel* with a thin cutting tool and cut slots in the heads of the bolts. Then use a flat ended screwdriver (impact if possible) to undo the bolts. Replace bolts.