Broken bow tang bolt...help!

Hey folks. I've had a bit of a disaster trying to remove the bow tangs from my Wave. I've managed to break the head off one of the bolts and I can't get the remaining thread out of the hole. I tried drilling it and using an easy-out, but that snapped off as well ...so now I have the rest of the thread and an easy-out that I can't drill (my drills won't even touch whatever material it's made out of) stuck in the hole.

What do I do now??

Progress update:
I got a carbide burr for my Dremel and managed to (very slowly) bore a hole through the centre of the broken easy-out and remaining thread. I got another easy-out in there, but it just broke the top few mm of thread off what was left in the hole. Trying to wind the rest out now feels very much like it's going to break another easy-out, which I definitely want to avoid.
I think I'm going to hit it with some penetrant and just wait a day or so and see if that loosens it up enough to wind the rest out.
Fingers crossed!

How it started:

How it's going:

Even with penetrant on it, the easy-out won't wind what's left out of the hold. It's well and truly seized in there

Looks like I'm drilling out the rest of what's left and chasing it with a tap to clean up the threads. Wow...I had no idea just how stuck a stainless bolt could get in a brass insert. I'll be making sure I use some lubricant on these when I put them back in...

Ok...it's fixed.

I drilled the rest of the broken bolt out and then ran a 1/4-20 BSW tap down the hole to clean the threads up. I've now installed new screws in all the bow tang holes, with some grease on them to hopefully stop this from happening again. Fingers crossed!