Photons having mass would screw up the Standard Model too... right?
Not necessarily. (Disclaimer: Physics background but this is not my area of expertise; I am working from memory of courses I took >5 years ago). In electroweak unification, there are four underlying gauge fields, superpositions of which make up the photon, W bosons, and Z boson. You have to adjust the coefficients of the combinations very carefully to make the photon massless and the weak bosons heavy. You could adjust them slightly less carefully and have an extremely light, but not massless, photon, without touching the underlying gauge fields; then y...
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.