Thanks for the comments both, looks like diluted PVA will be the way to go, and I do somewhere have a syringe from an old inkjet cartridge refilling kit that would be spot on for injecting it deeper into the crack. I did wonder whether CA might soak in and discolour the timber, and I really don't want to spoil that nice mahogany! Another thing I didn't mention was cleaning the fingerboard - I don't know how it got that way, but there's a load of grey-black gunk clagged all over it which resisted a wipe with white spirit. I may try warm soapy water and a stiff bristle brush, and if that fails the xylene will be coming out! I'm not quite sure what wood the fingerboard is, colour-wise it's the same tone as the rosewood back and sides (where it can be seen under the aforementioned gunk) but with a lot less figure to it.
As for finish, I'll keep chewing over what will be best - I do have a spraygun that I haven't used in around 20 years that I keep meaning to dig out, strip down, clean and try. on the other hand, maybe there is some merit in repairing the original finish. The machine head gears look a bit worn too, so I'll keep a look out on fleabay for a decent second hand set of Schaller or Gotoh classicals