What you're saying here doesn't make sense. You can't find out that something that's massless by definition
is massive. (And if photons are defined by QED, they are
massless by definition). What you can find out is that there's a theory that makes better predictions than QED. If that theory is a QFT that's identical to QED except that the spin-1 field is massive, then it would make sense to call the particles corresponding to that field "photons". But it only makes sense to say that you have "measured the mass of the photon to be non-zero" if you defined the word "photon"
using that class
of theories instead of a single theory. I'm surprised you keep objecting to that. It's not exactly a radical claim.
You seem to be replying to something very different from what's been posted in this thread.