IIRC, movement in spacetime is the same no matter which axis you designate as being time.
No. The metric treats time differently from space even as they are all on a single manifold. The Minkowski metric has three spacial dimensions with a +, and time gets a -. This is why space and time are different. Thinking of spacetime as R^4 is misleading because one doesn't have the Euclidean metric on it.
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.