I think Cortana should have Cortana in the background.... As in her face in the background at around 25% - 50% opacity, animated.... While the text and other information is presented in the foreground and more vibrant.
To give the impression of the stuff you want is right on the screen while Cortana remains inside and a part of the phone.
Simply adding transparency to existing UI, although somewhat effective in giving some life to the overall feel, really isn't all that unique.
Transparency is the new Lens Flare as Lens Flares were the Emboss, as Emboss was to Drop Shadows.
We need to think bigger.... We need to think More Cowbell.