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My suggestion is as follows: Make a 3D matrix (a tabbed set of tables would probably be best from a GUI standpoint) wherein a user can customize precisely which Screens, Desktops and Activities a window should be visible in.

Use case: in several of my Activities I like to keep an IM or email application fullscreen, they share the same Screen using different Desktops but in a combined "Communication" Activity I would like to have these exist on separate Screens but on the same Desktop.

This already works for activities. One app on multiple desktops and one app on multiple screens, well for those right now it's all or nothing. And I agree; that should be improved, if it can be done non-intrusively.