Interesting Question Regarding Voidsent.....

[Cleretic]

For example, what prevented the First from instantly becoming like the Thirteenth when Ardbert killed Mitron and Loghrif?

Minfilia.

Eden was a perfect kickoff for the First falling to an element, even if Mitron probably wasn't happy with the conditions; all a Rejoining takes is that, and a sufficient explosion of aether (be that explosion literal or figurative) on the Source to take it in. The Thirteenth is described as falling to a 'Flood of Darkness', so they seemed to face identical but aetherically-flipped phenomena.

There were a few contenders for the explosion to cause the Calamity; we stopped Thordan and Alexander, the Students of Baldesion stopped Eureka, and later on Gaius and Estinien stopped Black Rose. However, without all of that, the First was still on a death spiral that would've ended it like the Thirteenth until Minfilia yanked Ardbert's crew back to the First to halt the Flood of Light.

I am curious if the "salvation" they seek is in the same vein as Ardbert and company once did in that they intend to free the denizens of the 13th through death, though I'd think a rejoining is out of the question unless the circumstances have changed in some fundamental manner that makes the rules that once held no longer apply.

I'm curious where you're hearing 'salvation' from, because I just checked the scene with the Thrones and Obvious Golbez, and he says they seek redemption. Which is... still an interestingly loaded word to use, but one that's very different to 'salvation'.