The simple answer to your question is, and this is not intended to
put you down, don't even try.

The questions you ask suggest that you have little or no experience
with musical box repair and also that the box may be very seriously
damaged to the point of not being worth fixing in the first place.
Musical boxes, like fine watches, are precision machines and respond
poorly to household remedies.  Nevertheless my comments:

> 1. What is the best way to polish the brass barrel of the
> cylinder without disturbing the pins?

'Brasso' and a fine soft brush.

> 2. Is a clock mainspring barrel such as made by Hermle or
> Kieninger suitable for use in a cylinder music box?

Maybe, but probably not.  Springs are carefully sized to the size of
the movement and are generally more powerful than many clock springs.
Then, of course, the gearing must be correct.

> I have to repair one with more than 50% of the teeth damaged.

Depending on the degree of damage to the teeth, unless this is a
potentially valuable musical box, it is probably not worth fixing.
Tooth repair requires much skill and loads of experience.  Commercial
repairs are costly.

> 3. Where can I obtain the reduction gear set in a governor?

You may have luck with some vendors such as Nancy Fratti but, again,
not much is standard in this area so you very well may have to consider
having the wheels and pinions remade.  Not cheap.  There are professional
musical box repair shops that will service the governor for you.

Hope this isn't too disappointing for you and good luck in your quest!

Jim Heyworth
Sechelt, BC, Canada
james_heyworth@sunshine.net.geentroep [delete ".geentroep to reply]