The experimental upper bound on photon mass is 10^-18 eV. The photons near visible spectrum have about 10^-3 eV, which means their relative deviation from c is of order 10^-30. Gamma would be even closer. I don't think mass of photon is measurable via speed of light.
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.