If anything can travel faster than light, Einstein's theory needs modification (saying that the mathematics prove anything is ridiculous. The fact that the speed of light in a vacuum with no major gravitational anomalies is one of the bases the mathematics were trying to describe from). If your information arrives before the light saying it set out, while not exceeding the speed of light, there is no paradox, just a delay to factor into the equation. Theories, even those that have held sway for a long time, are open to modification - one of the fundaments os scientific method is that we will never know everything. Relativity might just have to edge over to make room for something else - it's had a good run. But a different means of getting from A to Z without being obliged to traverse the entire alphabet is also non-contradictory.
Faster than light travel only ends up as time travel if you accept the paradigms of relativity, and if anything can travel faster than light, these are wrong, and require editing.
No sweat.