If you can get it up onto a vertical mill a centre cutting carbide end mill should do the deed by cleanly removing the core leaving the thread behind as a sort of spring shape for you to pick out. 3 or 5 flute ones can be found. I used a 5 flute one to shift 4 (I think) broken 2.5 mm taps. Lost a flute on the last one but still finished the job. £5 or so to save many hours of work seemed a bargain. Stainless should be easy in comparison.
Down at those small sizes HSS needs a bit too much babying to keep the cutter in one piece especially with dissimilar materials getting in on the act should a bit of run out occur.
Clive