Well that went fairly badly.
I've made a tap, all bar the square on the back end anyway.
Two issues… Firstly both corners chipped off the thread cutting tool – one after about 10 thou of cut and the other towards the end. I cut a bit deeper which should hopefully put the untidy part of the profile in a place where it will do no harm.

The bigger and more puzzling issue is that my 0.0406 thou tool managed to cut wider grooves somehow. The threads measure a tad under 1mm rather than a tad over. I'm not sure why so that does not bode well for being able to correct the problem.

In spite of the issues I decided to finish off the tap and cut the flutes using a 3mm ball end mill in the Potts Spindle. There was a 40T gear on the lathe spindle so I decided that four flutes seemed like a good number. The square for the tap wrench is still to do because the poor little Unimat motor was getting rather warm.

The tap almost certainly won't work for an unworn feed screw but hopefully I will at least be able to find out if the tap approach can produce a cross slide that actually works, albeit still with a worn feed screw.