Thanks to everyone that gave me advice on adjusting my music box.
The advice was very valuable and much appreciated.  You'll be happy
to know that I took your advice and did not adjust the governor and
suffered no run.  You also educated me on what the other screws were
for and why they should not be touched.

Using a fine 1/2" wide paint brush and squirt bottle with a needle
applicator, I did clean the bedplate and gear cluster/governor and
cylinder bearings with fast drying naphtha (a mild solvent which is
basically lighter fluid), being careful not to get any on or in the
pinned cylinder.

Then I lubricated the gear cluster with a super refined clock oil that
I purchased from an online clock repair supplies vendor.  To my
surprise, the music box works as it was intended and plays the 8 airs
all the way through and the governor even starts by itself without
having to be flicked.  Your advice saved me from making the bad mistake
of possibly subjecting my music box to a devastating run.

No one ever gave me any advice on how to safely polish the pinned
cylinder without damaging the cylinder, so I assume that is something
that is just not possible as I cannot imagine how it can be done, so
I will have to be content with a tarnished cylinder that plays
beautiful music.

Thanks again, everyone.

Jim Patrick