Progress 1 Spindle(?) : I bent it :(

[slim_boy_fat]

Lateral thinking - I thought it was obvious?

I meant the 'drill in the chuck and making decreasing sized 'scores' until it was right' idea, no-one else suggested it. But the important thing is, it's sorted to the OP's satisfaction.

 

[rockweasel]

Final Update:

Drill back together. Managed to drill a round hole the same diameter as the drill bit. Nothing caught fire or fell off. Job done.

 

[pressbrake1]

You can’t cut a precise enough taper on most hobbiest lathes to mate together.

You’ll have to recut the taper as near as you can, then use blue and emery tape, till it’s spot on.

If you’ve got a junk chuck with the right taper you could use lapping compound.

To set accurate taper id put drill chuck in the lathe and clock in off the taper to set the compound.
Even on a toolroom machine with taper turning I clock off a master where possible

 

[Seadog]

he following day I took a trip along and presented my greasy quill to the receptionist.