Let's put it this way: without time, events do not occur; without space, things do not exist. Quantum non-locality works out that two connected/related/intertwined particles can communicate instantly regardless of distance between them. To do so, information must be 'traveling' many multiples of "c" if the objects are very far apart. There is only one way I can think of for this to be so and that has to do with the actual nature of time (time is a function in speed, as you know). Time is thought of as a linear phenomenon, which can be warped by sufficient gravitational field. It may have other expression characteristics, also, like planar and volumetric. Planar time may be the 'time' reality for the photon, but you're not interested in such stuff ... because you already know what cannot be true, as if you have already proven the negatives you wish to hold onto. ;^)
“Um, wrong. If there is no inertia mass then regardless of how fast it travels it does not accumulate more mass.”
That is also an irrelevant point, because even something with zero mass cannot travel faster than c.
“Quantum non-locality works out that two connected/related/intertwined particles can communicate instantly regardless of distance between them.”
No, quantum non-locality explicitly does not allow FTL communication. It involves, as Einstein famously noted “action at a distance”, but that action does not pass any usable information, so it doesn’t help you in your quest to violate relativity.
“There is only one way I can think of for this to be so...”
This sums up the problem right here. Just because you can’t think of another way, you assume things must be the way you think they are, but you are mistaken on quite a few points.
TIME is Mother Nature’s way of making sure that everything doesn’t happen at once.