I wonder if replacing it with a nice wipe-on polyurethane would
be in order. The stuff is decidedly moisture/oil proof, easy to
put on, and seems (mostly) harmless.

I just used it to finish my new oak stairway rails and after
about eight cyles of sandpaper, finish, dry, sandpaper, tack-rag,
finish---   it's awfully nice.

I think I'd pick the 'satin' finish for the neck of an instrument.