The argument about 'but what if they were just trying to sacrifice a bunch of chickens to Zodiark, you don't know' honestly kind of misses the real point of the whole thing. The problem with the third sacrifice wasn't necessarily what they were killing for it (although again, the story doesn't play if it's not something big), but that it was the point when they were no longer willingly sacrificing themselves to help the planet, but rather forcing others to involuntarily sacrifice lives for their own comfort. The world is safe, peaceful and functioning again, and yet that is not enough. It's even going against the wishes of those sacrificed; remember that we heard from those souls in Mare Lamentorum, and they are still completely okay with their own sacrifices. The third sacrifice is for nobody's benefit but the surviving Ancients, as well as the point where the notion they might ever be satisfied is gone.

To a degree, you could say that the moment the third sacrifice was hatched was the point where the Convocation became the Ascians. The point where all reason beyond a selfish desire to want their perfect past back is gone; the point where Emet-Selch's stated view of 'I don't see you as people, so it's not murder' became their accepted view (and yes, I know that after a point he didn't 'really' believe that, but there was undeniably a point where it was true).