Maybe Saya was going to be a replacement for the Master Unit or maybe she is a Chrono Phantasma(Doubtfully) of OPFD Noel, or maybe a planned Vessel for it(Could explain her very high are magus aptitude). But I guess they needed a change of plans and used her for Izanami instead, but because of her high aptitude made it difficult for Izanami to dominate the body. So Relius "customized" her to fit better to be Izanami's vessel. Though Saya is possibly desperately trying to kick Izanami out, but all effort is in vain though it might be the fact that she mixed to much that helps a little to.
Maybe due to Izanami forcibly possessing Saya without a pact as Saya was against it and the fact that Terumi "broke" her mind allowed Izanami forcing herself in Saya's mind, due to Saya not being compliant to it in the first place.
Though I might be looking into this too much, I could be wrong.