Hello Clay, I think I can solve your problem.  There is a fellow near
Rochester who does wonderful woodworking and finishing.  He's done a
number of music box cases for me and several friends.  He also restores
pieces for some of the local museums.

Replacing the stringing and missing veneer on your lid should be a
cinch.  I'll send you his contact information.  I was going to post it
in this message but I wanted to ask him first and he's not in today.

Regards,
Craig Smith