I was reading the thread about tap extractors, thinking neat stuff.
Was gonna post my solution, but held off, my way seemed kinda primative.
I cleaned the tap off as good a possible with a pick (loose material bits and pieces), tap tap tap with a punch (try to lossen it up a bit). Took a pretty thick piece of welding rod (copper coated for acytelin welding) put a little dab of flux on the end of the tap and used the old buzz box to weld the rod on. Kinda held my breath thinking I was gonna weld the tap to the threads, but it worked for me.
I´d try a coupe of trial runs first. Have used the same technique with 24 volt battery voltage in the military.
As a last resort, it my be an option. A shot of Tequilla (medicinal), will help the nerves and steady the hand.