It's not really soul manipulating, it's not as if Shizuka could bring back the dead. It's more like setting up a save point. If or when the Angel of Death will resurrect Miyu, Miyu would return to her body. Of course if her body is completely destroyed, then a new one is made back wherever she belongs. Effectively, "deleting" the save point. Alternatively someone else can try to consecrate Miyu's corpse, akin to overwriting the save except now someone else is doing it instead of Shizuka.
So as long as Shizuka can maintain her consecration ritual and make sure Miyu's corpse is still suitable for life once Miyu is ready to resurrect, Miyu will come back to her body. And it just so happens that her body is with the Machina.
Also how can Miyu invite everyone to her birthday party without sending invites? Angel magic only goes so far. I bet the Machina are the only ones who maintain the internet and postal service in the Nexus. Plus with the Mecha Maids you don't have to worry about cooking and clean up. And think of all the wonderful toys Miyu could get if she celebrates her birthday with the Machina! All the gadgets and mechs she could ever dream of. Of course she can't actually play with any of them, what with being a prisoner of war, but Hibiki could set her up with some wicked sweet VR that would make sure Miyu gets stuck in a lotus-eater machine.
@TheWindel I'm sure Shizuka realized what sort of a sin she committed when she defected from Heaven to be with her sister. But Shizuka doesn't really care; as long as she has her family no god or devil will bring her down.
