Soak the bolts with penetrant. It might get into the threads to loosen it up, it might not, but it doesn't hurt. Center punch the bolt to keep your bit from wandering and then use a 1/8" drill bit to drill a pilot hole down the center of each bolt. Follow with the largest drill bit that won't get into the threads. Use an extractor. Use your senses. If the bolt isn't turning, but the extractor is flexing hard, stop. You really don't want to break the extractor off in the hole.
If it doesn't want to come out, use a solid (not spring loaded) center punch and a small hammer. Try and spin the bolt remnants out by pushing it around with the punch and hammer. You'd be surprised how well it works.
The last resort before the machine shop is to try and use the center punch and hammer to collapse the outer shell of the bolt inward to loosen it.
I almost forgot that I shot a video on this.
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