You might not even need to remove the head. If you can get a hardwood dowel into the plug hole, try tapping it with a hammer. If it doesn't break free, give it another shot of oil (I like Kroil), and try it again the next day.
I had a 1939 BSA M20 that was stuck when I got it, and had been so for several years. Daily Kroil and light tapping with the dowel & hammer freed it in about a week.