Looking for advice on how to tap some stainless.

[Voicecoil]

I will add to that:
1) Use the correct tap for the job - you can get special taps for stainless and other troublesome steels, the ones I was recommended have a green ring on them (from Europa tool IIRC), and I've yet to break one.
2) Whilst I would agree with Mekanik's advice if you're using straight flute taps, an alternative approach is to use a spiral point tap for through holes and just keep going slow and steady. The rationale behind this is that stainless work hardens rapidly and that the only way to keep on cutting into soft metal is to always cut into fresh metal. I did a number of M6 holes in a 10mm slab of 304 (I think!) this way with no problems at all.
Logic would say that for the blind holes a spiral flute tap (again green ring) would be best, but I've not tried that and wonder if they would be strong enough. I guess if you're good at contortion you can also put the work piece upside down and tap from below if you want to be super-careful with swarf removal!

http://www.europatool.co.uk/pdf-down...ation-taps.pdf