I wish I could help, but conservation is not my purview. Most museums would treat it as mgl mentions, without water washing or solvents but with gentle dry cleaning. But museums prize irreversibility more than anything in conservation, and don't want to remove finishes. If you want them bright and clean again you may want to go further, and for anything more serious I'd recommend a conservator. I like the idea of calling the university nearby you that has a conservation lab to see if they have any programs in which they could use this as a practice or demo item.

I love mgl's spit idea. I don't know if it would be bad for the threads, which are the most delicate - and most strategic - part of the whole thing, but it certainly works on the beads! If we were on Mecha Island, I would have a spit party.