I finally found an academic article that discusses the cat piano! Micheal John Gorman, director of the Science Gallery, contextualizes the cat piano within the Baroque culture of machines and the early-modern obsession with torturing cats (that's right, cat torture was a bit of a craze). Apparently the cat piano is believed to have been invented by the Jesuit polymath Althanasius Kircher (no surprise to anyone remotely familiar with this guy). Schott and Kircher were both interested, among many other things, in the strange, exotic, and wondrous side of nature. Gorman's article focuses on the spectacular array of marvelous machines (for e.g. the water-vomiting two-headed Imperial Eagle machine) that Kircher displayed in his Musaeum Kircherianum (part of the Collegio Romano) and the space they occupied between legitimate and illicit magic. The cat piano, however, seems to have been more of a playful early-modern joke (despite the um... animal cruelty aspect). Gorman cites another study that treats the cat piano, Instruments and the Imagination, which I have yet to check out. I guess that means stay tuned for another installment on my bizarre fascination with this oddity!
Update #3: Video of a modern cat piano for Prince Charles!