I recommend installing tuners with a body-ward downward angle like an SR. Interesting bass.Well! The parts cleaned up OK. I set them aside for the nonce.
The plastic nut hath arriven. I have a brass nut underway from China, but this one will do until then.
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You can also see why I thought this was a shorty when I put it in the gig bag.
I work on old rusty bicycles and second the vinegar recommendation. Let that dry and then try the WD40 and PB blaster etc.