I went back to the slaughterhouse to capture an animal I had missed, and now I can't exit through Slaughterhouse Entrance, since the code for the gate doesn't work anymore.
Am I just missing something, or does this really mean I have to start the game over? I really don't see an exit out of this. It would be a shame, because the game is great otherwise.

You don't have to enter the code again since the gate is already open.