Well, I had been ill since Thursday, nothing major - just a lurgy but ill enough to mean I didn't get around to sorting out the tuners until today. I won't bore you with a complete step by step - the results of polishing are great but the process isn't exactly a spectator sport. But to give you an idea of the amount of difference I was making...
Anyway, very long story short - all tuner parts rinsed of cola, dried, polished, reassembled and greased. Frets polished. Fretboard and headstock polished. Tuners reinstalled - had to put some cocktail stick and wood glue in a few of the holes as the screws were just spinning. String tree polished.
Doesn't look that shiny now, but it looks a damn sight better than when it got here. And I don't have to wash my hands after tuning it up, so that's a bonus!