Well depending on the lay out of your house and the size of the puppy crate, just crate the puppy in a room with a door that closes, close the door (with the cat NOT in that room) and then there will be no more playing of animals. I imagine you could wedge a puppy crate into the bathroom even if the rest of your house is open plan.
I used to have problems with sleep when my cat was a kitten because if I shut him out of my room, he'd wail mentally outside my door. And if I let him in my room, he'd be so happy he'd sit on the back of my neck and purr INCREDIBLY LOUDLY into my ear. It was annoying.
I don't like dogs, so I don't care on the crating issue one way or another. Guessing orchestral doesn't have an issue with it or they wouldn't have a crate for the dog.