Alright, I have some success with pof-cob-pof. I found out you need to manually set which model is which LOD, and delete the LOD's that won't have any models.
That makes the ship work in game with it's new size. What I still didn't figure out is why does the rescaled model have the same height, width and depth as the original one (while all the subobjects show are rescaled, and the game sees the ship rescaled; I think it might have something to do with global importing everything from the original model, I'll try another rescale later with manually adding everything and see what happens), and if it has any effect on gameplay.
I'll post something when I figure this part out (but I don't have any more time for this right now, so it might take me a while...).