Hi guys,
Fergus - I did test it before I launched my little rebuild, and it was similar to now, ie chattered a lot.
Steve - yup, I'm concious of that, I can't see any cracks but if I do order new bearings I will fit them to the spare head just in case.
Doc - when you say the chuck is 'sprung' what do you mean sorry? Are you referring the the jaws not being parallel?
So I've just been out and done some more tests. I managed to tighten the spindle bearings more by extending the spanners to give me more leverage, I think the rear bearing is too tight a fit on the spindle, as it took a lot of force, but doing so has reduced the end play to half a thou and got rid of the bearing noise. Also, it has introduced a bit of drag and for the first time the bearings are getting warm.... I can still deflect the spindle nose by about 0.01mm by pushing on a 200mm test bar though.
However, I think I've got to the main cause of the issue. The chuck just isn't rigid on the spindle nose.
I confirmed the shoulder on the spindle nose (which the chuck butts up against) is running true, and has no burrs, nor does the back of the chuck where it hits this shoulder, but the chuck body can easily be deflected up and down by several thou just by pushing on a 6" workpiece.
Putting a tailstock centre in makes it turn perfectly, I can suddenly take a 1mm cut on a steel bar and get a good finish.
The issue seems to be therefore that the workpiece is wobbling because the chuck isn't rigid on the spindle.
I checked the chuck was bolted tight to it's back plate, and inspected the spindle threads really carefully, can't see what the problem is though

Surely if the chuck is butted tight up against a true-running shoulder on the spindle, and there are no burrs, it should be tight and rigid? Unless it's just the small amount of deflection in the bearings being amplified?