I don't think that's quite right.
The faster ship has time pass more slowly. So they all leave at the same time, traveling a light year, but one ship travels at 0.999999 C and the other at 0.5 C.
The faster ship doesn't notice hardly any travel time...
Yes it does. Remember, relative velocity is only meaningful with respect to an arbitrary fixed point in space. If you're moving towards an object that is traveling in the same direction, only 100km/s slower than you, then your velocity relative to this object is 100km/s. If, without accelerating or changing directions, you then measure your velocity relative to a photon torpedo someone just fired at you, you find your relative velocity is now 250,000km/s.
If what you say is true, the amount of time dilation you're experiencing would depend entirely on what you're using as a reference point: there should be no noticeable time dilation while you're chasing the stolen shuttlecraft. There is also no time dilation when someone fires a photon torpedo at you... but the moment you SEE the torpedo moving towards you at near-lightspeed, time suddenly grinds to a halt.
It doesn't work that way, and I shouldn't have to explain why. But just in case: you do not know and CANNOT know how that torpedo happened to be moving towards you at 250,000km/s. Your calculation for Delta-T is therefore true whether the torpedo was fired at you at that velocity, or if it was fired AWAY from you at 200m/s -- say, by that space station you're about to pass on the right -- and you're just moving so incredibly fast that you're about to crash into it.
So when it arrives, it's clock indicates that perhaps a day has passed
No, nearly a year has indeed passed. From your point of view, EVERYONE ELSE seems to have slowed down.
Again, the effect is only manifest while they're moving with respect to each other. When they match velocities again, their world lines reconverge and the clocks are in synch again.
You've got to remember the thing about relativity: all measurements are subjective.
Conditions in YOUR reference frame cannot be altered by what anyone else observes, your frame is always true for YOU, so no matter what velocity someone measures when they look at you, in your frame, you're stationary, and time passes normally.