The main problem with 3) is that if photons have mass, then we would observe differences in speed of light depending on energy at least as big as the difference measured now for neutrinos. This seems not to be the case and c is measured with very high accuracy. If photons traveled with some velocity lower than c, but constant independent of energy, that would violate special relativity.
Yes, but we almost always measure c precisely using light near the visible spectrum. Rough estimates were first made based on the behavior of Jupiter and Saturn's moons (their eclipses occurred slightly too soon when the planets were near Earth and slightly too late when they were far from Earth).
Variants of a Foucault apparatus are still used and that's almost completely with visible light or near visible light.
One can also use microwaves to do clever stuff with cavity resonance. I'm not sure if there would be a noticeable energy difference.
The ideal thin...
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.