I'm kind of hoping that sprawling research facility beneath the tower is involved somehow.

Between the new Weapon project and the Solus clones, the Garleans were up to all kinds of questionable things down there and it wouldn't surprise me if something instrumental to Anima's initial summoning was included in that because even given the sheer amount of faith from the Garlean populace and a catalyst in Varis, there's still the matter of where the requisite aether for the summoning came from...unless I missed something.