Using a dremmel with cutting disk -
Try cutting a slot into the top of the carriage bolt - this will turn it into a "flathead screw" instead of a carriage bolt. Then you can use a large flathead screwdriver to hold it while you back the nut off.
I use this method to remove phillips head wood screws that have become stripped. (Wood screws strip so easily, that's why I love drywall screws)
Cheers,
Craig