Maybe were saying the same thing here.
I'm not trying to say the math will be invalid. Is that what you're trying to say here?
I'm trying to say the predictions of the theory will be different, if C is not an invariant.
ds^2 = -c^2*dt^2 + dx^2
Think about the physical interpretations and predictions of this equation with c constant, as we currently think about it.
Now, take c as something that is no longer invariant between inertial frames. Do we have the same outcomes from this equation, or from our theory in general. I don't think so.
How would natural units even work, which would make c=1 in the equation above, if it was variable, which it would have to be if photons have mass?