get to the back of the bolt?
It doesn't sound like it, but can you get to the back of the bolt? sometimes there is enough stuff sticking out the back and if the head is already busted off, you can screw it IN all the way through easier than you can screw it out too.
(just thinking outside the box)
Also, sometimes you can get the broken off ez out to wiggle just a little bit. That is often enough to get it to suddenly fall out of the hole. I've done it more than once with drill bits in cast iron and a couple of EZ outs. Things that looked tragic suddenly were fine.
Oh yeah, I have a crystal bolt extractor in my holistic automotive healing kit you can borrow too. Just arrange the crystals around the bolt and by the next full moon, the bolt will extract itself.