What the hell? Okay, so I just beat it without really realizing how. Somehow EMPTY IS ICE followed by ICE IS YOU lets me walk through walls? I don't understand why.
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On L9 I could change what WALL IS, but I can't do that on L12. They're up against the side, so there's no way to change WALL IS STOP, FLAG IS WIN, or BABA IS YOU. All I have to work with are ICE, SLIP, and EMPTY -- and all I can make them IS is WALL, STOP, BABA, YOU, or each other. Another tip? Sorry that I'm dense.