I originally thought the SN1987A results--which show the neutrino burst from a supernova in the Lesser Magellanic Cloud arriving at the same time as the light,

I originally thought the SN1987A results--which show the neutrino burst from a supernova in the Lesser Magellanic Cloud arriving at the same time as the light, within error-would easily falsify this but forgot that high energy tachyons approach c from above as their energy goes up, so for the 5+ MeV neutrinos that were detected the velocity difference would be negligibly different from c regardless if the mass is positive of negative. It's a curious result, but I'd still lean toward consistent defects in the data over a tachyonic neutrino, personally.