I strongly prefer it when the Scions *don't* have Ancient counterparts.
I think it means more if they're part of the new souls born to the star either after Zodiark's first summoning or after the Sundering. Which is a whole thing!
Importantly, those were the souls that the Convocation were going to sacrifice to Zodiark to bring back the Ancients they lost.
To me, I think it's vastly important that G'raha, Y'shtola, Urianger, Thancred, the twins, that all of them are people Emet-Selch would throw away without a second thought. That to him, you're the only one worth half a damn... And broken as you are, only half a damn. And before he lets himself accept that you really are what's left of Azem, you're just someone else he's convinced isn't a person.
But I think these are the very souls Azem left the Convocation to save, even if Azem still didn't want to break the world. And these are the souls that Venat and the Twelve did break the world to save.
To me that's so much more important than any reincarnation romance (much as I adore that kind of story too). That to Azem and to you, these people matter anyway.