Core/Freeze Plug blow out

OP, so the plugs blew out when you got on it? By any chance, do you have some mild, persistent overheating? If so, there may be a combustion chamber leak into the cooling system, like a head gasket leak, or head crack. Just a thought.....

Your research on the slightly large plug sounds like a good idea. The fact that the first plugs dropped most of the way in is a sign that they were too small. They typically fight you all the way in. You should use a thin coat of #1 Permatex or similar on the edges.