From the pics, it looks like the part of the plug with the nut is loose and detached from the thread (?) Heard of that happening on very old cars, never actually seen pics.

I can't tell if that is the electrode with the tip of the plug that is sticking out. If so, there would be a small hole into the cylinder, and the reason why the cap flies around is because the pressure from the cylinder escapes through the hole.

If that is the case I would not drill this out, because particles of ceramic material will end up in the cylinder, and I don't think there is any way to avoid getting them all out and not scoring the cyl. walls. For the same reason, I would not drive it at all.

An easy-out will have nothing but ceramic material to grab onto, so that may not work either.

I think you may have to pull the head, and do it on the bench. Titanium coated drill or a small chisel, then a ez-out or bolt extractor, and even after that you may have to put a sleeve into the spark plug hole because the threads may be damaged.