I have used almost all of these methods, except for the EDM and acid, with varying success. I have always had the best results with a carbide end mill. Of course, how many home shops
have carbide endmills? Probably a small percentage.
Another method I have used is to shatter the tap with a center punch. This works pretty good if the tap broke because it is brittle or improperly heat treated. The center puch should be a good tool steel for it to work.
Prevention is the best course of action. Buying cheap taps will get you into trouble, as they aren't as sharp and might be brittle. If they aren't sharp, they will jam and break. Also, backing the tap out until the "chip" breaks off frequently will help keep the tap from jaming, and of course use plenty of taping fluid. Examine your tap for broken or chiped teeth before you start