I will say, as a point of clarification, the Elysian capitol system and their homeworld was not intended to be moved; rather, their other systems would be shuffled around/moved/etc. Currently, Elysia Novus is in a spot easily described as "awkward", a capitol world isolated in its own political island compared to Yamatai and Nepleslia. That being said, I'm also open to additional options being discussed - to be topical to the current narrative, the Kuvexians might attack from the "north" and take over systems in the area Legix had drawn around (and some other systems in that general area, of course). After the Kuvexians get pushed away from the Kikyo sector there may be a "hole" in that area.
Or perhaps, some Mishhuvurthyar remnants try to start up a mess in those systems with all the focus on Kuvexia, and this would give the bigger nations a reason to actually try to trust the prissy angels with something - "clean up this infestation and the planets are yours" basically.
An alternative idea for this would be that the Kuvexians attempt to make a device similar to this - after all, they are incredibly powerful "bad guys" - but with the aim to weaponize it, literally throwing a star system or three at Yamatai in an attempt to wreak havoc and potentially destroy key systems that are keeping the catgirl nation together... But the tech simply doesn;t work right, and they "miss", the stars and maybe some of their planets make it through in a relatively intact state but the device they used ended up destroying itself mid-use and the star systems it transported are damaged/made incredibly unstable.
Of course, some minor retconning to move certain systems around would work but it'd require some fairly thorough wiki combing to ensure properly updated information exists.
We could pull a Star Wars, where there's a star system that doesn't exist on the records, if we wanted to, as well.
I dunno, honeslty - I'm just throwing ideas at the wall here. I think that planetary and stellar relocation, especially over vast distances, should be extremely rare no matter what. Even these incredibly powerful civilizations can't build one easily, cheaply, or quickly.