Walking off screen was originally pointed out by capnshrimpy in a meteor police run. I stumbled into a way to repeatably set it up when despawning Edna in the kitchen. It seems like the character you're controlling off screen must move extremely fast as I was able to traverse the security hallway and up the stairs pretty quick. I've been messing around trying to see if there's someplace it can be put to a decent use.

Hilarity ensues... This is just getting silly. I love it.

Wow! Does it need a capture/cutscene to initiate? I'm wondering if initiating new kid and switching during a room transition might break it as well.

I haven't been able to do it on a screen transition by itself, or transition to the pause screen. Getting caught by Edna seems to be the easiest way to set it up. I'm starting to think it's all smoke and mirrors. Looks cool, but might just be wasting time. That's a lot of screen transitions there, and not much progress on movement. I'm not real sure about it at the moment. Neat to see and thing about though.