I don't think it much matters if the storylines don't quite match up. As long as they have the same underlying themes. I mean, if you were to make a continuation of the story each time, well, how many times can you flee a planet and recolonize another? I don't see much wrong with having slightly inconsistent sotrylines, where they're all sorta like "possible truths". It could be that this is all the same ship from the same time period, but a slightly different story for a new game. I mean, common, look at what Final Fantasy has done. I ca't think of any sort of coherent storyline linking the first 7 games (I haven't played past #7 really), but they did all have the same sort of underlying mood to them.
But yeah, if you have a storyline that works, then go for it. But if there are holes in the story, I don't think you need to worry too much about filling them in.
Btw, I think I rather like that second starship idea. Sounds pretty good so far.
