Ah ok I see what you're getting at.... That might require some serious coding - by all means correct me if I'm wrong, but because there isn't transparency there already then the desktop wallpaper would be disabled, allowing the application background to take over....

Alternatively, replacing the image with the same image as behind the menu screen (ie; the blurred desktop background) would have the same effect. However, this would only be a single image fix rather than a transparency effect.

I don't think that the phone works on transparency because to smooth the desktop transistions you remove the blur applied to the main desktop background - meaning it's not a transparency, its an applied effect.

Not knowing enough about the set up I can't really comment tbh.... Sorry