What about disassembling the bodies for the trip?
Upload the crew's minds into a suitable computer, break the bodies up into cells, accelerate at whatever rate the metal can take, reassemble the cells by stored patterns back into crew's bodies, transfer minds back.
Problem solved.
No... you just killed the crew and cloned them.
In a way that would be very, very difficult to do.
I don't know if someone already written a post like this... I haven't been through the 9 pages of Star Trek we have going here...
The easiest way to ask yourself what defines a human is to ask yourself this:
Would you still be you, if you woke up in another person's body? If your body was lost and you transfered your mind into another body. Although you'd have to get used to your new body, you would still be yourself.
So, if the only real identity you have is your mind, then your body might as well be a robot. It's just a vessel to carry your mind.
As such, the method described by Artlav wouldn't produce a "copy paste" person.
A bit off topic, but the follow up question is:
Does "pasting" a copy of your mind into two separate bodies make a single person? The answer is no. The moment you create another copy, that person gets their own identity. Even though everything until moment when they got copied will be identical, everything from that point on will not be...