You are doing it all wrong
Hey, I thought this was all sorted out already, with no real need for fantasy physics. In just a few decades from now we will be able to travel pretty much anywhere we at the (perceptual) blink of an eye. Basically, you serialise anyone who wants to travel. Store them in a massively redundant form in a dense, robust and stable substrate, I dunno say a chunk of quartz or something. At which point you have you perfect solid state astronaut. You can shoot him around the universe will little fuss. No need to waste energy accelerating a live support system, shielding, food, toilets etc. and he can take silly-g without becoming pâté.
Ok great, now duplicate him/everyone and fire them off in all directions. You can spend a little energy every now and then and boot up a virtual image to take a look around and make a course correction etc. Once you see a place of interest you spend the other half of your budget on stopping near a good energy source, build a big array of radio telescopes as a relay station, duplicate and send off another burst of seed ships. We can exchange diffs via the relay network to keep the whole lot coherent. Pretty soon the whole of humanity is a RAIDed cloud spread across a massive volume of space that is expanding at close to c.
Just try and wipe us out then you bastards!
The really cool thing is that we can play with our own clock speed at will, to fast forward through all that crawling about at c and then speed up to enjoy the good bits. Like downloading into a new body to enjoy some snu snu on Amazonia.
Serialisation gives you all this plus a whole lot more without the need for Trek style make believe. No new physics needed just a few decades of technology and neuroscience and we're off! I'd strongly suggest checking out some of the novels by Charles Stross to get all the details.
BTW if I kick the bucket before this all happens, I am going to have an extremely rude message to future humanity carved on my gravestone. That'll show them.