It's common that light speed is surpassed for the sake of the plot. Even light speed is rather slow if you wanna get to stars. Alpha Centauri is four years away.
Yet I have found a way to still do it. With zero wait time. If I'm not messing with light speed, I have to mess with something else. Namely, time and energy manipulation.
Fire a teleportation beam at light speed, teleport spaceship with it, crew will arrive whenever beam reaches it's destination at light speed.
Normally time diation would kick in. But it won't. Because time will be messed with.
Namely, the base planet will be frozen in time via a chronoton field (fictional particles of time). Not a bad thing since it's not like the inhabitants will know anyway.
The ship could take 400 years to reach it's destination, yet they won't feel the time difference, since they only appear on the other end after teleportation.
It may take them 400 or perhaps even a 1000 years to get home depending on where they are.
But it won't matter, because time will be frozen on their base world when they return. And then they can unfreeze it, back to how it was with none the wiser.
So this is a trick, a way around beating life speed and aging all at once.