If you have a butt end of a carbide end mill, grind a sharp cornered 4 side pyramid at 60 and running the mill wide open (and that won't be too fast, use light pressure and cut down the middle. Use an end mill just large enough to clear the flute's root. The remaining "teeth" will fall out. Use air to blow away the chips, which will be very, very hot. That's how it works. Extremely negative cutting angle, very strong edge generates enough heat to soften the HSS and cut it away. Just kind of peck your way through. If you want, you can use a round scribe type punch to flake out the teeth as you go if you want.
Hardest part is getting a more or less flat break on the tap to start with. This worked on larger taps as well. Can't tell you how many 1/4-20 taps I've broken in Inconel and titanium, and other exotics and drilled right out like that. I keep a few carbide "tap cutters" on hand, although I haven't needed one lately. Just remember, carbide is not very flexible, so if you see it try to deflect, move the part around to minimize that. Also, it helps to use the quill at near it's full extension and don't let the lock drag. You want a bit of slop there too.