How would this work?

Render your cyclorama background. Save that render and then load it as a background image. Load the other items as before (but not the cyclorama this time). In your render settings, make sure that  'render over background' is enabled and render the picture. The objects in the scene should cast shadows (which should be caught on the ground plane as that is set up by default to be shadow catch only) but wont cast shadows onto the cyclorama background image. If necessary, increase the size of the ground plane to cover all of the area that your scene items are on.