On the bright side, a huge mess of soap suds is, of all the huge messes that could wind up spilling halfway across the kitchen, pretty inoffensive, and totally hilarious. Also, it turns out that dishwashers make AMAZING bubbles -- very dense and fine and long-lasting.
Extra thanks to longueur for the baffled and friendly, "Is there some reason there are suds all over the kitchen floor?" and the cheerful cleanup job. Sadly, he didn't think to snap a photo first.