I've found an interesting bug in Aftershock.
If you need to move your Laputa to start a mission and you don't want any time to pass. in the mission pop-up press the "move laputa here" button then immediately save the game without disturbing anything.
If you now quit and restart Aftershock and load the saved game and restart the clock by pressing the space bar your Laputa should have instantly moved to the destination, so you can stop the clock again and start that mission.

I'm playing on windows 7 64 bit and the above method works reliably you may need to try a few times though so be patient.