Technically, does it even matter how fast we eject? Shouldn't relativity allow us to reach speed of light with any positive thrust velocity? If the speed of the shuttle was of any concern, that should directly invalidate relativity, since passengers would suddenly not perceive any acceleration anymore, even though nothing about the spaceship and its physical reaction has changed.
"Folding space"/"Warping space", or shrinking the space in front of the craft while expanding the space, would seem to be the only theoretical way to achieve speeds that not only would match light speed but could surpass it and not break the laws of physics as we understand them. The drive Alcubierre proposed in the 80's, I think... maybe the 90's. I'm not sure when. A Spanish mathematician or physicist who was a fan of Star Trek.
EDIT: My understanding of physics is pretty minimal. I'm more than happy for someone to correct me and explain what I got wrong. This type of stuff is fascinating.
From the perspective of an outside observer, a constantly-accelerating spaceship will approach the speed of light, but never quite get there. This will happen regardless of the level of thrust.
Alcubierre drives are pretty sweet - the only trick is they seem to require negative mass [0]... at least they've gotten down the requirement from a negative Jupiter mass to a mere -700 kg!
[0] - https://en.wikipedia.org/wiki/Alcubierre_drive#Mass%E2%80%93...
As for the rest of your second paragraph: Look into how relativistic velocity addition works.