I intended to reassemble the spindle and its cluster of gears, spacers, and taper roller bearings myself, but after talking to an expert on the topic (Swen Pettig), I realised that sometimes it is better to leave surgery to a surgeon.
I gratefully accepted Swen’s offer to help. In his working life Swen had performed this task on many, many occasions.
Firstly Swen reinserted the taper bearing outer races in the headstock. The lathe spindle is approx 80mm diameter and 800mm long so it is heavy. After careful cleaning, it was fed into the headstock, progressively loading the bearings, gears, spacers, clips and nuts, and moving and tapping them down the shaft as it was moved into place.
when it was all reassembled and tightened, the retaining disk at the chuck end was loosened, sealed with liquid gasket (Loctite product- cannot remember the name), and retightened.
Then Swen went through a lengthy process of checking the end play, using a dial indicator, tapping each end of the shaft with a copper hammer, and finally settling on 0.01mm of play.
Then we had a short test run at low speed, and he tested the end play again, with no change.
Then we set it running at 200 rpm, and went and had a cup of coffee for 20 minutes. Came back and checked the bearings temperatures. All cold, all good.
I reinstalled the external gears, the cover, etc, and took some decent cuts in some cold rolled bar.
All good. Oil change soon.