This:
"turning to 2.9 mm and have a nice 45 deg. chamfer on the end, open up the die for the first pass"
and This:
"and shouldn't be overtightened. In fact, I only ever use one screw, not all three"
worked for me.
Opening the die – quite a bit actually – has stopped it 'overcutting' the small rod i turned. I now have a workable thread. Bit of a result really as I really didn't want to be shelling out for a new HSS die and hoped the steel one would work. It can now go into the drawer for the next millenia to come along when I might need it again.
This is the problem when you are spoiled with first class kit and you buy something "on the cheap" just to get you away on a job. I really should know better. Not to worry, something else I have learned. Bit of a result really.
graham.