Given more thought about this, I realised that there is already that slow, but efficient FTL drive - it's the one everybody uses anyway. If we assume Domain of Man had something like several mountains' worth of telescopes and other measurement devices devoted to monitoring stars Orion - Perseus, as well as much more spent on computers, it might be possible that they've predicted trajectories of the majority (if not all) of stars and similar massive objects between the arms and thus were able to accelerate XIVth in the hyperspace to significant velocity, sending them on a trajectory to the Sector that they'd arrive slower than if they were using fuel to overcome gravity pull of all those stars and just go straight through, but it'd be massively more efficient since they need to use it just to slow down at the end, and half the fuel is typically used to accelerate in the first place. This is more or less just a standard sublight speeds interstellar travel, except in a hellish dimension where gravity seems to have an inverse effect on the space, it being naturally (and relatively to normal space) contracted and tiny, but gravity would expand it significantly, which means that it conveniently means that empty spaces are much less of an issue, but at the same time complicating aforementioned sublight travel techniques. We still have inertia, though, so we're good to go.
That hypothesis was, obviously, shot down by the fact that XIVth isn't cryogenic now, which means they're travelling a much shorter distance and thus their arrival after gates were shut is illogical. Unless DoM collapsed on a civil war and they were sent off in a slower way so that they wouldn't intervene. Or DoM just set up an experiment without them knowing; the fact that this particular Sector didn't receive any signals even after 200 years is suspicious.