Hello McFly,
We do not merly say "time would pass more slowly for the crew of the ship than for those still on earth?" - it does.
The people on earth have "aged more" relative to each other.
I'm not sure if this answers part of your your question, but I found this regarding the speed of the Earth/Solar System:
"If you have a good idea of the Sun's distance from the Galactic center, then the solar system's speed can be approximated. Using speed measurements of the gas at different distances from the Galactic center, the Sun appears to be cruising along at 200 kilometers per second and it takes 240 million years to complete the grand circuit around the Galaxy. This speed is an absolute speed." Source
Also, there have been a couple famous experiments proving Time Dilation:
"In 1971, experimenters from the U.S. Naval Observatory undertook an experiment to test time dilation . They made airline flights around the world in both directions, each circuit taking about three days. They carried with them four cesium beam atomic clocks. When they returned and compared their clocks with the clock of the Observatory in Washington, D.C., they had gained about 0.15 microseconds compared to the ground based clock." Source
And another link
Anyway, I need to do more research on the topic, but I hope I answered your question(s) and at least made you scratch your head.
Something to think about over the weekend/the next couple years. ;-)
See ya, Vince