I've read this thread with interest because I have handled this kind of problem many times. It is aluminum oxide having migrated molecularly into the threads to create an unbelievable grip. It is also so tight that it is nearly impossible to soak any kind of penetrant or lube into it because it isn't very porous. It would be interesting to see some cross-section views of all of these methods to see how far the penetrating lubes were able to get.
I've almost always had to drill out and retap. Sometimes when the drill has exposed some of the threads those other solutions can get in to do some chemical work.
And on the idea to use air-pressure on a stuck piston out of a cylinder head, I just want to chime in against it as too dangerous. The same effect is better done hydraulically with better results and less explosion and less flying pieces of metal bouncing around the shop.