Would it violate any special laws, if someone were to change the axiom of SR that "Speed of light is the same with respect to all reference frames"
To
"Speed of light is the same with respect to all reference frames, but it's own reference frame, where it is the minimum".

I can then assign the photon a rest mass. Of course, it will get a reference frame as well. With no direction, time or mass or speed. I mean if I got in the concept of 0 here, then it would be possible to assign the photon a rest mass, and say that the photon exhibits both these traits.

The mass trait, not part of an EM field.