Thanks for the many suggestions! Jim I'm not sure if it's encouraging or discouraging that your device didn't work either .
Making the part by cutting an M6 thread onto the head of an M4 allen bolt is an interesting idea, I hadn't thought of that. An M4 bolt on its own wouldn't work, the way this part works is the difference between the pitch of the M4 and M6 thread is used to either jack open or close up the slotted part of the base, to tilt the column over.
It has occurred to me that in use, the portion of M4 thread nearest the shoulder (save for the last couple of mm, which are also unused) is actually in use – and due to the taper of the die, this is also the portion of thread that is least well-formed.
So if I simply reverse the die and cut it as far as I can go, that might salvage it without having to remake the part. You can see in my picture that the last few threads are chunkier than the rest.
Failing that I will have another go at this part, and try Bizibilder's suggestion of using the tailstock to push the die square.
Edited By James Stanley on 01/03/2023 18:09:45