I found the secret ending! You can get to the broken teleporter without dying by using both cats! It's embarrassingly easy, though. I was way overthinking it.
Something like how far away does the cats need to be when they enter the room; which sections of the map do the cats use; which cat gets to the teleporter etc
Sorry to EveTheEevee, you probably won't see this. But for anyone else who does, the cats have to be lined up so one cat follows the top border while the other keeps it alive. This lineup has to start two rooms back.
I like the secret ending because the goat represents the developer. The goat sees you do that, thinks “oh, that’s not supposed to happen” and pushes you into the teleporter.