Well, literally moments after writing my last post, with my fourth party (who all really knew what the were doing), I finally conquered the Lady of the Vortex.
(spoilers)
For a moment there I thought that the Primals were actually going to WORK TOGETHER, which I thought was fundamentally impossible. Looks like I was right; Ultima Weapon (I presume) happened instead. A magitek monstrosity that bitchslapped three Primals in quick succession, each one a horrible ordeal to fight for any sane mortal, and then absorbed them? I have to fight THAT?! *whimper*
You do, and it is worse than you think.