Tried the Dremel/unscrew method, it didn't work. Easy enough to make the groove with the Dremel, but the bolt wouldn't budge, and I ended up shearing off more of the bolt.
I will see if there is enough room to file down the sides and use Mole grips, but given how it seems to be stuck fast, I think I'm going to have to drill it out.
I've seen mention of those "Easy Out" extractors on some web pages, with people saying they often end up breaking those too.