Nice idea. mansion stage in Dishonoured 2. I think the unresponsive controls folks mention is directly tied to the short delay just after switching. When rapid switching matters (like the stop-start level and the last level), they need to respond immediately. Perhaps solved by moving the both player characters and only applying death effects when the screen in which the death effect is present is visible.
Another issue I had was that the game appears to have been designed and intended for a much larger screen than is present on MacBooks. I had to move to a different machine to play the game.
Played through and had fun, though.