Lol, you are no scientist. A real scientist would know, do not depend on math, use your imagination, imagination is better than math. There a high probability (thats right, probability) that the mathematical equations are incomplete and also a higher probability that any assumptions we make to establish and solve the equations will lead to a wrong answer.
I use good math. This is bad math:
Light takes 8 minutes to move from sun to earth. If you are moving at twice the speed of light that means it will only take 4 minutes to move between the two. So no you will not arrive before you leave.
True from the sun's frame of reference, I suppose. Very cute.
Show us your math please then, enlighten us.
Grab the relative simultaneity equation, screw around with it until you get a delta-t' that isn't zero, and pretend you have instant teleportation between the different frames of reference. That will give you an idea of what happens to causality at FTL speeds. You don't even have to do the Lorentz transformation yourself. Just google "special relativity equations". All you have to do is algebra. You can do algebra, right?
The accuracy of whatever you caclulate is experimentally verifiable to about fifteen decimal places. Any new theories of relativity will give you the exact same answer, no matter what we discover in the future. Beyond those fifteen or so decimal places, maybe there's room for a better equation. But never in the future of mathematics will a new theory give you a different answer within that degree of specificity, or else it's wrong.
If this isn't enough to convince anyone, then you may as well believe the Earth is flat.