Oh dear. I think the head will have to come off. If you attempt to drill it in situ, you may end up with swarf on the piston just waiting for an opportunity to slip down the gap between the piston and barrel or to jam a valve open. Even if you take the greatest of care, you'll never really be sure will you?
With the head off, you can drill the centre out of the plug. If you use a left hand drill you might be lucky and get it moving that way. More likely though, it will need heat, penetrating oil, heat, penetrating oil etc, heaps of patience and a good stud extractor. There are several informative videos on Youtube by the way.