That matter can not simply be brushed aside and ignored if you want to move other matter through space.
You are correct on this point, and I was agreeing with you. You should have stopped right there. The rest of what you have to say is nonsense:
Travel frames of reference as pertaining to time are debatable outside of the sublumial construct
Wrong. There are objects in our universe beyond our horizon which have apparent velocities greater than light because of the expansion of the universe. We can no longer see them because the light from them can never reach us. Lorentz invariance applies to these objects.
accepted mathematical principles laid down by Einstein
They were not laid down by Einstein, but by Poincare, Lorentz, Fitzgerald, Minkowski, and others. Einstein's contribution was that he understood the physical significance of the mathematics.
simply due to the fact that he did not believe any appreciable quantities of mass (such as a ship carrying a pilot) could travel faster than a photon
He did not believe anything. He proved that it was not possible.
the energy requirements to propel such mass at such a velocity would exceed the mass of the universe itself (at least I think it was Einstein, I could be mistaken).
You are mistaken about what he proved. What he proved was that a particle with a finite rest mass -- even something as small as an electron -- would require an infinite amount of energy to reach the speed of light.
Traveling backwards in time is not feasible according to known laws of physics, quantum or otherwise.
This statement is probably true, but not proven. Neither in classical nor quantum physics has this been proven. There are a number of speculative theories that deny it, or argue in favor of it. There is no known observation that it is impossible, nor is it inconsistent with any existing theory. The laws of both classical and quantum mechanics can be run either forward or backward in time.
In any case, traveling faster than light does not necessitate moving backwards through time.
Yes, it does. This statement is 100% factually incorrect.
The mathematics at that point are very debatable.
No, they are not. The mathematics required to prove this requires nothing more than the two principles of Special Relativity and very basic (right triangle) arithmetic. I have taught this to junior/senior undergrads in Physics, and although I haven't used my PhD in Physics for almost 30 years, it has not changed, and I have not forgotten anything this basic.