If what you are really interested in is a detailed model of a tonewheel organ, why don't you just measure the movement of the gears in an actual device? High frame rate video and audio acquisition doesn't seem difficult. You can also experiment with replacing the springs in the photo.
Heh! Exactly that had long occured to me, sure it would be nicer to only replicate the action where it happens, not all the stuff before that.
But for that, you'd have to actually have such an organ. Do you have an idea how monstrous those things are? And not exactly cheap either. If I had a house, I might buy one, but I haven't ;)