This dichotomy ignores another possibility: That the filaments are not, in fact, moving the ship at all in any of the three spatial and one temporal dimensions we’re accustomed to dealing with. We have absolutely no indications that these pockets are physically contiguous with the normally-observable universe.
While this possibility is an extreme and radical thing to suggest, I can’t help but feel that at the very worst, it is no more radical a suggestion than the idea that adding a single 10m3 device to existing warp engines will suddenly completely alter the way they work, and produce a level of FTL travel that is many orders of magnitude greater than anything our best theoretical models can produce.
Additionally, the transfer conduit created by the so-called ‘space-time filament’ (which means what, precisely?) is clearly not a 4-dimensional structure… so there’s no reason to believe it initiates four-dimensional movement.