Well, I broke a tap yesterday, and had it out in less than 20 minutes - simply by recalling and taking the list's advice rather than doing all the things that I normally do first, which never work...
On at least a bi-annual basis I for some reason try to chase the threads in a blind hole that I can barely reach (on my race car) forgetting that the hole ( always in a rare, irreplaceable aluminium casting) has been previously helicoiled. This time I broke a 3/8" tap at least 1/4" deep in the hole. I immediately ( after cursing for a while) got the mig welder out and started to build up the broken tap to where I could weld a nut to it. The heat loosened things up, I backed out the tap and the rest of the now defunct helicoil, chased the empty hole and installed a new helicoil. total time to repair - 30 minutes!
Thanks, all, for the good advice.
Cheers, Brian