Its hard to manual tap small holes where the tap tool cross section is so small. I can literally snap the taps with my bare hands if i wanted to. My tap was also really brittle. I think it failed because of material fatigue since I wasnt really putting too much force on it any different than the other operations.
I bought another brand of tap and tried again, this one 2 flutes instead of 3 so cross section is larger. Its also HSS and not coated. Seems to be better as I now finished all the taps. I also changed the style of tapping, I rotate the tap maximum 120 degrees when hit with mild resistance when tapping, then I back off completely, clear chips in tool and hole and repeat. Small taps require more babysitting.
Yeah, Im gonna throw another carbide at it and then I will give up. I will try the helical approach. The problem is, the end mills dont have enough reach and my threads go really deep. The tap is stuck deep. I think EDM is really the only approach but I dont have a commercial machine. DIY technique works but slow and now recirculating flow to flush dust away. This is quite important as it stains your part. Now my part has brown stains from the eroding of the steel tap.
EDIT: I just got my hands on a 1/16" 4 flute TiAlN coated end mills. This stuff works. My other plain carbide 1mm broke. This one is eating it away, although I can only have enough space to do plunge milling. I lost one of the flutes that broke off but Ive managed to mill out quite a bit. although the threaded parts of the tap is still locked in.