Most of the monkey grinder acts I have seen in recent years use a very small barrel organ of a single flute rank. I suggest using a large scale flute. Though it would be best to have a small amount of chiff, I have heard this effect done quite well on theater organs using the Tibia rank without vibrato. You could use the free Paramount sample set for this.
The real trick is learning to play it like the arrangements that are used for the barrel organ. You could listen to recordings - I believe there are some available.
As for the "music box," there are actually many kins so I would not know how to start without more information.
Les