For those of you who, like me, have been looking at data and scratching your head wondering why two rotations in a row of Haumea don't match even when there is no mutual event going on, I now strongly believe the answer is that Hi'iaka rotates with an approximately 10% light curve and an approximately 8 hour period. Hi'iaka is usually within the aperture for the photometry, so this gives an additional 1% light curve to Haumea at an 8 hour period. The effect looks frighteningly like a mutual event. If one knew the phase, period, and amplitude precisely one could subtract it out and still see mutual events, I think. But finding those paraemters requires more observations when there >aren't< mutual events, rather than when there are. We might have enough data from all of the observers to be able to piece something together though.
The moral is: this will take much more work than initially anticipated, but it is (perhaps) less bleak than it appeared when the data didn't make any sense.