How about the Scharnhorst effect as a possible explanation? It would essentially amount to photons travelling slower than c in vacuum because of a small vacuum refractive index due to vacuum polarization, which the neutrinos wouldn’t see, so even with a small rest mass, they could conceivably travel faster than photons in vacuum; this would also be in line with the 1987A neutrinos being slower, i.e. closer to the photon speed, due to their lower energy…