You have spent some time and effort with some nice example, but I have never written, that because the measurement of neutrino gives c, that is means that Lorentz factor equation or relativity is wrong. I have speculated that there is maybe some other, better equation, which could give c for neutrino. And because of the margin of error, my speculation cannot be ruled out either. It does not rule it in, or in other word it is not a confirmation of my speculation, but it simply can not be ruled out based on measurement. Theoretically in future there could be some measurement where the theoretical speed difference is clearly above the margin of error, but we have no such measurement as of today.