Wow, yeah. I finally figured out how to get onto the secret path you mentioned. Especially devious that a large part of the path is actually just open space in rooms that you go through early in the game.
I figured the extra-wide doors were important, but it took forever to realize that the starting point of the path wasn't an extra-wide door. Sneaky sneaky @epicpikaguy...
I can't seem to pass the top exit of 11,16 though. Every approach I try ends up with a cat sitting on the 0-flag, so I can't step out the exit. So close. I'm starting to think I need another cat - but I don't think I can take a third cat into that level, and I assume I shouldn't need one since there's a shortcut into that level that wouldn't have it.