You could go with virtual stages, one for each part in the 'main' stage, and put all mappings for those in a 'background' scene, which is always active.
Each real scene will only contain a 'projector actor' for each mapping, sending the image to the virtual stages and this way to the 'background scene', where the actual mapping takes place.
You could do it in each scene, straight from multiple 'projector actors', without bothering virtual stages and 'background scenes'. But this way you simulate what you wanted to do in the stage setup, keeping the full potential of the first stage izzymap functions.