We can approach this problem while avoiding all those annoying "you can't"s by considering what would happen if your magical space ship accelerated to almost c

We can approach this problem while avoiding all those annoying "you can't"s by considering what would happen if your magical space ship accelerated to almost c in one minute. The answer is that the distance from A to B would be length-contracted, and would take (from the traveller's point of view) very little time to traverse. In the limit, once the traveller has reached the speed of light, the entire universe in front of them contracts to zero length, and they (from their point of view) can cross the entire universe in no time. Like a photon, they would experience no time between achieving the speed of light, and hitting something. From the point of view of planet A and B, it still takes a whole year for the traveller to make the journey.