I have found liquid wrench to be a very useful tool when working on things like that. While I am not quite sure exactly what is remaining in the head, it sounds like the ceramic is still connected to some piece of metal with threads. Try putting liquid wrench on the threaded area, give it several hours (or overnight) to soak and see if the offending plug will come out using your finger (or maybe some needle nose pliers).
Another alternative is to use an adhesive, such as JB weld to bond a rod onto the plug. Once the adhesive has set up, the rod can be turned with pliers to remove the plug. If that approach is used, don't put on liquid wrench until after the JB weld has cured.
If drilling the plug for the ez out looks like the best path, once you hit the ceramic it will break. If it doesn't fall into the cylinder you are good. If it does, then maybe a tube connected to a shop vacuum might get it out. A borescope would be very useful then.
Personally, if this isn't a diesel and the liquid wrench w/finger/pliers did work I'd just pull the head. While it may seem like a lot of work, you will never again put a steel plug into an aluminum head without anti-sieze. Of course, an alternative is to have the car towed to Bubba's garage where they will charge you $500+ for getting the plug out and may still leave debris in the cylinder.
Sometimes, what should be a very simple job turns out to be difficult.
Good Luck!
Malta