OK, if earth is not going to define the frame in which time is absolute, and now you think there is something very strange about this frame, you need to tell us exactly how you are going to identify this frame. Saying that the future as well as the past and present are cast in concrete, doesn't help, you need tell us where is this frame. How fast is the earth or the solar system moving through it and in which direction?
In your example, you didn't tell us the speeds of the ships with respect to this absolute frame, you just took a relativistic approach and said there was a difference in speed. And you didn't define the time at which the twins popped into existence in terms of an absolute time frame. You've got to decide if you want to promote an absolute time realism or a relativistic one. Please be specific. Tell us how you are going to identify the absolute time reference frame. No more fuzzy ideas--that won't get us anywhere.
Imagine instead of ships we have identical chunks of radioactive material moving at constant but different speeds in straight lines, no one knows exactly how fast they're moving relative to each other. Clearly if the difference in speed is great time dilation will seemingly notably affect half lifes. After a time their composition should thus measurably differ in such a way that it would be possible to order them in terms of speed differences, and to tell which rock was the slowest amongst them all.
If they were on a collision course the nature of the collision would be affected not just by differences in speed but via the differing composition. Reaching the same destination at different speeds should thus result in different stuff*(compositionally) arriving at the destination. IF the stuff was originally identical, the one receiving it will be able to note compositional change and thus be able to tell and compare the speed at which it came.