Success!
Held the valve in the 4-jaw with the head behind the jaws and cleaned up the groove with a Dremel in the toolpost & a fine grinding wheel. It took very little to restore it to round and cylindrical.
I was scratching my head trying to work out how to establish the outer taper on the collets and then to cut it. The former I achieved by filling the collet with Plasticine then measuring that as the internal dimensions were tricky to measure accurately.
Then set up an old HT bolt in the 3 jaw chuck and used the compound slide to set the angle. Did this by setting the cross slide to zero at the end of the blank with the tool touching the blank, then winding the compound slide along till the length was correct and using the cross slide to wind in the tool till it touched again. I could then read off the lateral distance.
I thought that would be much more accurate than using a protractor.
Then turned the taper, drilled (6mm, the new diameter of the recess in the valve), parted off then sawed the resulting part longitudinally on opposite sides. Cleaned up and it fits very well.
It wasn't as hard as I thought it might be.