Hi,
That looks like an interesting project, but you have to be careful so that the solenoids don't damage the moog. An alternative would be to connect some wires directly to the buttons inside the music box, but I guess that is not an option since it's a vintage instrument.
Anyways, I have quite a lot of experience with Arduino. Depending on the other peripherals you need to connect to it, you might need to mux the solenoids or else you might run out of pins.
Ramiro