I want to use different wallpapers for each desktop on the cube, which I know I can do by setting different activities for each desktop. But that forces me to re-create all the plasmoids on each desktop when I want the same ones on each. Also if I then change one, I have to change them all by hand.

Is there a way to have just one activity or set of plasmoids shared among all the desktops, but still have a different wallpaper on each?

Unfortunately it appears that the current design of Plasma does not allow this.