The NEXT trick is managing not to kill the crew from all the radiation generated by traveling very, very fast through a space full of - radiation.
Who says you have to travel through the space? Why is everyone assuming they know the physics of something that we have no clue how it would even fundamentally work? A bunch of armchair physicists suggesting theoretical problems to things that we have no clue about. How about moving the space - and everything in it - around the ship instead of moving the ship through the space? How would something like that work, you're asking? We have no idea! Just like any hypothetical you're referring to or making up!