I have a different theory on the origins of Amata and Kagura.
I won't go in the details about whoever comes from Altair and whoever comes from Vega. There aren't enough evidence for even the the assumption's base to properly speculate.
Instead I bring up something from the original Aquarion series.
If you didn't watch Sousei no Aquarion (that I assume are relatively few in numbers) then read the spoiler above at your own risk.
Anyways, in short I theorize that the soul of Apollo and Apollonius reincarnated separately.
Amata = The reincarnation of Apollonius
Kagura = the reincarnation of Apollo
That makes more sense IMO than claiming both Altair and Vega has the reincarnation counterparts of every important character.