What follows is my experience with servicing the spindle on my lathe. I urge you to approach this with caution - if the spindle or bearings are inadvertently damaged, things are going to get expensive. Many thanks to Tony Watson and Neville Chase for sharing their experiences with me - it allowed me to proceed with confidence. In addition to this document, you may also want to read Neville Chase's experience with a roller bearing spindle since there are clearly similarities between the two.
Disassembly
There are any number of places problems could occur with the spindle. With mine, a burr had formed around the small hole which the pulley grub screw 'C' locks into. This was preventing the pulley from spinning freely when using the backgear. I filed the burr off and ensured the pulley would spin freely. The front bearing also showed some scoring, however there were no raised burrs and I was in no hurry to pay a machine shop to engineer a solution so it went back in as-is. It ended up being fine.
Reassembly
To assemble, simply reverse the disassembly procedure. Other than the fact that the shaft has several steps that catch just as you're trying to push the shaft through a new piece, it is quite simple.
I was very worried here about breaking the bearing caps. Fortunately all went well. Loose, my front bearing had 4-5 thou of movement. The rear bearing had significantly more movement but only in the vertical direction.
First attempt, I tightened the front bearing down to around 1.5 thou of movement and the rear bearing to a few thou. I adjusted the end float as tight as possible while still allowing the spindle to spin freely. The results weren't too good, I was always working to avoid chatter.
Second attempt, I tightened down the bearings some more. I left the end float setting the same. The front bearing now has very little movement and the rear movement is barely perceptible. The spindle still spins freely by hand and the bearings do not get hot when running. Performance of the lathe is now great. Attempting to cut too much (or too quickly) simply results in strong resistance against the tool, whereas before chatter would be guaranteed.