Now that I know how to do the tangents properly, the XSI mod tool has decided to not work in my favor .. or .. at all. I suppose it's because it's been unsupported for so long that it's simply incompatible with newer systems, even in compatibility mode.
The only exception is when I create a blank new scene, put the model in, create second texture and tangents, only then I can pick the second projection without error. But only once. Touching the tangent generator but one extra time makes xsi go invalid call and there is no way back from the loop.
I tried reinstalling XSI, also tried the different version, but apparently the problem is the same in the old script, so the the error seems to remain identical through all mod tool releases I put into my computer.
For now I'm gonna try installing and running XSI in a virtual machine with WinXP, to see if that fixes the problem.
Anyway, here's a screenshot of the ship working in game, but having poorly attached tangents:
EDIT: Virtual machine didn't help fixing my problems with XSI, but I managed to somewhat resolve the tangent problems anyway - not sure how, but I eventually got the projections set up so the ship is decently shaded. It's far from perfect, still has issues, but it's acceptable now.