To throw my two-cents in as far as the Mu-12 thing goes, while I wait to see how they go about it in the game? I'd say the best way to look at this is the whole Gaara thing in Naruto.
He lost his tailed beast, but was still really strong and could do sand-based jutsu and his absolute defense was still as good as before. Until we get an in-story reasoning behind Noel's ability to use her Murakumo side? I'll just say that she's not as powerful as she was before after being untempered by Ragna, but can transform the same way Nu went into her battle armor. Thanks to Rachel of course.
Why think so hard about why and just think about her being able to get it back to use for good?