Ah- I finally managed to get those patterns memorized enough to get through. For people having trouble with the zipping pianos, the best way to get through I could figure out is:
Room 1: The piano moving up and down (and by the corner) moves the slowest and is the easiest to dodge. Move to just south of it and sidestep when it comes down until the keyboard blocking the door moves down, then dodge around it and out.
Room 2: Immediately move two steps up, then run left and down to where the bottom-leftmost piano had been. This is a safe spot. Just wait for a few seconds for the rest of the pianos to crash and make your way out (careful not to touch any of the broken pianos though, they still kill you for some reason).
Final room: Simply sprint upwards and to the left before a piano blindsides you from behind. Exit stage left :)
Also, I recommend going to the settings and switching "Always Dash" to On. Otherwise these quick movement things are almost impossible.