If you are faced with having to scrap the blunt taps, you won’t lose anything by trying using freehand a grinding-point or small grit disc in a hand-held “micro” power-drill (a ‘Dremel’, ‘Proxxon’ or similar).
Grip the tap shank in the vice, and use both hands on the tool for best support and control.
Note the flute is undercut a touch to give a cutting-angle to the tips of the thread. Examine a reasonably large, sharp tap to see the geometry.
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Similarly with a die, provided you can get a carborundum point into the side holes. If not, a lap made from a bit of brass or aluminium rod with fine grinding-paste on it, may do the trick.
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I must admit I’ve not attempted this myself, but have often pondered it. I have wobbly hands though, and yours might be as steady as a neurosurgeon’s or a clock-maker’s!