I think so; with any noticeable faster than C, can't you just ping-pong between paired receiver/emitters, gaining a little distance into the past with each ping-pong? (If you're only gaining a few nanoseconds with each cycle, might be expensive in equipment or energy, but for the right information from days/weeks in the future - like natural disaster warnings - it'd worth it, even ignoring hypercomputation issues.)
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.