I like your thinking and sounds like you had it under control the whole time.
It was hard to tell by the photo, that is alot bigger screw then I thought. I bought a torque driver set and it has saves me a number of times. I think that is what they are called anyway. You hit it and it uses down...
You could try a masonry or carbide tipped drill bit, just to get thru the casing of the bolt, then move to a high speed drill bit. Once the head of the bolt pops off, the pressure will be off the threads and should come out easly...
I can't see for sure, it appears to be a Button Head Cap Screw, or BHCS.
Any Way, take a pin punch.
Get a hammer.
Put the pinpunch at an angle towards the edge of the bolt head.
Hit the bolt at an angle towards the Counter Clock wise position.
You might have to make a spot on edge...