I'm betting on the local structure of causality.
Not necessarily, there could be a distinguished frame of reference.
That might preserve before-and-after. It wouldn't preserve the locality of causality. Once you throw away c, you might need to take the entire frame of the universe into account when calculating the temporal successor at any given point, rather than just the immediate spatial neighborhood.
http://www.nature.com/news/2011/110922/full/news.2011.554.html
http://arxiv.org/abs/1109.4897v1
http://usersguidetotheuniverse.com/?p=2169
http://news.ycombinator.com/item?id=3027056
Perhaps the end of the era of the light cone and beginning of the era of the neutrino cone? I'd be curious to see your probability estimates for whether this theory pans out. Or other crackpot hypotheses to explain the results.