Some great ideas here.
Another thought is to actually have two different AI's on the ship, each having their own objectives. Perhaps the players only uncover the presence of the second AI as they are trying to deal with the first one. One AI could (appear to) be more benign, the other quite erratic/nefarious (i.e., one appears to be more lawfully aligned aligned, the other chaotic). Each AI tries to manipulate the PC's to achieve their objectives, which naturally conflict with one another. This makes for some interesting dynamics in terms of the PCs needing to take a side (or not) - with all choices being morally grey.