What klhansen is describing is the idea of drilling the heads with a drill bit that is slightly larger than the shaft of the bolt. When the drill bit gets to the shaft of the bolt, the head will just come off because you've drill through the underside shelf of the head. Then, when the parts are on the work bench, you'll need to get the rest of the bolt out.
Before trying that though, another idea is to drill a small hole into the bolt and use a left-hand tap to dig into the bolt and unscrew it..
Let us know what eventually works for you.
Cheers, Dean
