Here's a different take, if a time traveller was to go into the past by surpassing lightspeed he might end up in the future. On acceleration he/she would eventually have to pass through the light barrier where time and distance mean nothing. Upon deceleration he/she would also have to make the same pass. So, all that travelling placed him/her at the light barrier twice, if only for a moment. So as he/she further decelerates to a stop there is advancement into the future.
Maybe the only way to get into the past by exceeding c is to never slow down to lightspeed once past it. Don't think you would see much or even know. Don't take this post too serious, its just for fun.