The team of reserves was assembled and ready even before they had managed to finish modifying the shuttle that was going to take them through space.
Calling it a shuttle was a bit of a misnomer, as the ship was large enough to be a private yacht. Most of that was due to the need for it to have a dual-drive system, though. One would bring it to half cruising speed, without using a Warp Field, and then engage the Traction Drive to bring them to Warp 2 once they were free of the turbulence.
But the Traction Drive was not meant to be used at the moment. Instead, it was a backup to get them out of any region that they encountered where the standard Warp Drive was inoperative.
Once they were free of this star system, they should, in theory, be able to use the Warp Drive to get where they were going while remaining cloaked at a much higher rate of speed.