Buy suitable sized bolt extractors and use those. They look a bit like tapered screws with a coarse, reverse thread. You drill a hole into the centre of the bolt, screw in the bolt extractor and as it tightens up, it undoes the bolt. , assuming it isn't well corroded in place.
I last used these to remove the Philips-headed bolts from the allow crankcase of a Honda motorcycle gearbox - which meant being very careful!