There is no such thing as time. Time is determined based on our own frequencies and perception. We see 24 images per second. How fast you are traveling isn't going to change that.
If you were to see more than 24 images per second, then time would start to slow down in appearence for you, and everyone else would not feel it. This happens in accidents and such and is proven that you can see more stuff when your brain operates at more than 24 images per second.
Furthermore, speed is relative. According to the above theories, 1 side of the earth should happen faster than the other etc. As the sun spins around the galaxy, and the earth spins around the sun, and as the earth rotates on it's axis, then when you are on part of the earths spin that is in sync with the other movements(as a sphere, 1 part of it will always be there), and then on the opposite side of the earth you would be traveling slower on the universal position.
So, the entire thought of using speed to go faster than the speed of light to time travel is really nothing more than changing externally the amount of images per second to give the perception of time travel.
Just think about it like a movie. I'll use the matrix as an example, since they did alot of time slowing in the movie. For the majority of the movie, it sends you the same amount of images per second that is in sync with our own perspective. So what is physically happening when the show slow motion parts? They are sending more images per second to you than would be normal during the movements(of the movie's perspective), and thus gives the appearance of slower time.
So IMO, going faster than the speed of light is not going to time travel at all. You're brain will still be processing at the same frequency and the same images per second, only if you are going that fast it's only a distortion, not actual time travel.