The only people they want to "save" are those who are already gone via Zodiark; everyone else, including the souls currently alive, are merely fodder to bring them back.
1/4th of the Amaurotines were never sacrificed to Zodiark to begin with, and like most of the Convocation members must exist as sundered beings in the current sharded world. We can say then that the Ascians are invested in rejoining everything's souls at least for this 1/4th of their people as well as to return the sacrificed.

This was the entire impetus for the summoning of Hydaelyn, because the dissenters went "no, this is not acceptable, we cannot cling onto our civilization at the cost of everything else".
The Anyder actually say nothing about any of this when discussing their motivations for summoning Hydaelyn amongst themselves. They say they intend to summon Hydaelyn because the summoning of Zodiark didn't bring a permanent solution to ending the threat of the Sound. We don't know what that entails, why they believed this or what if anything they even knew of the Sound, but they don't really say anything about the Convocation's intent to sacrifice proliferated life being relevant to their plans.

But Emet-Selch (named specifically by Mitron, but again I suspect Elidibus would also be eligible) didn't even bother, because doing so would mess with the one-track plan he had for Rejoining the First through Light.
This is what he says, we have no reason to believe he's correct. It's true that the Unsundered considered the sundered Ascians as being expendable, because from their perspective they can simply be reraised once again at a later date, but as to his belief that Emet knew his situation, Emet himself says that he believes both of them were slain and that he is the only Ascian on the First.