By far the best way to remove difficult-to-reach broken taps is EDM. In a few cases I ask a friend of mine with acces to a wide selection of EDM equipment to do this. However I first try to use a HM drill. As most taps are HSS a HM drill will cut them up. As a regular full HM drill is rather costly I take a cheap stone-drill which has an HM bit at the top and I regrind it to cut HSS. This works quite often.
Another application for reground stone-drills is piercing the sometimes quite hard skin of castings.
Another application for reground stone-drills is piercing the sometimes quite hard skin of castings.