Let me make some corrections to your post.
Firstly the Lorentz factor is not used to prove the speed of light is a maximum.
Its origin predated SR and was used as an ad hoc explanation to explain the null result of the MM experiment while preserving an absolute ether frame by suggesting that objects shrank in the direction of motion.
Einstein derived the Lorentz transformations in SR based on the postulate the speed of light is the same to all inertial observers, not as a speed limit.
The context is the speed of light in a vacuum - which is implied to be not only constant, but a maximum of c in all inertial frames. The math being used to get to part of that conclusion is the Lorentz Factor - which is source-independent. That is the problem, not whether or not it is a limit - the self-independence of the critical velocity.
Note in GR the speed of light is not an upper limit as the recession velocities of high z galaxies indicate.
The Hubble Constant is seriously flawed. But I admire GR.
Secondly combining SR with QM was a problem in the 1930s not now as explained in
this post.
For the rest of your post there is absolutely no experimental evidence for the existence of a “superluminal inertial frame”.
Every single phenomenon that may have pointed to superluminal velocities ranging from a practical application of the
lighthouse paradox to the phase velocity of an EM wave exceeding c has found no information transfer is possible.
That there is no experimental evidence for the existence of superluinal inertial frame is a testament to our crude physics - not to its impossibility. Have we been able to reproduce a galaxy in the lab to test its dynamics in the same manner it would occur in real-time nature? That doesn't stop the mathematical theory from evolving things we will/hope to see later on (things we are incapable of realizing now, for whatever reason).
Here is a video that goes into somewhat more detail as to why the no communication theorem prevents superluminal velocities for entangled particles.
Ok. Let's create an example that is in the middle - an
alternative (where one front is superluminal, and one is not); we don't even need the particle to be superluminal for this example. Define
alternative as
superluminal if both fronts are superluminal, and
semi-superluminal if only one front is superluminal.
Lets say in "world" M1 there is a photon sent from the Earth (call this event E1) to arrive at a distant star at some moment T1 by the clock of that star. Let M2 be the world that was
initially the same as M1 but instead of the photon assume the "Enterprise" is sent (the start of the spaceship is event E2). On its way to the star the spaceship "warps" and tears spacetime by travelling very fast passing stars, merging binary black holes and triggering other imaginable powerful processes.
We are still assuming no tachyonic matter.
Despite all of this, the spaceship arrives at the star
later than the photon emitted in E2. However, we can still entertain that the spaceship arrives in time T2 less than T1. So, the speed of the
spaceship in one world (M2) would "exceed" the speed of light in another (M1), which
would
not contradict the non-tachyonic nature of the spaceship. It also wouldn't break the ‘light barrier’ in M1: the inequality T2 < T1 implies the front (call it N1) is superluminal, but no matter signal in M1 corresponds to the front. Particularly no spaceship in that space-time is associated with N1.
These two "worlds" would be considered the
alternative of semi-superluminar speed, and if one can accept these conditions it shows such an
alternative allows "superluminal" signalling without tachyons.
Its "superluminal" character does not contradict the principle of causality in M1, because in the space M1 (Minkowski space) the surface N1 does not correspond to any signal. The front N2 is not superluminal, so the alternative is semi-superluminal. The spaceship reaches the destination at a moment preceding the arrival of any photon emitted in E1, but no tachyons are involved. Even though the photons are in M1, the spaceship belongs to the universe M2, where its trajectory is timelike.
If/When we get the opportunity to build a spaceship like this and test it, we would be inclined to confirm what we would have already known.