But why do you want to duplicate the entire scene?
You only need to duplicate props which receive a shadow from invisible character.
Render your scene normally (without invisible character, or make it invisible at the timeline where it should be).
Set background to white (in Project settings).
Hide everything except duplicated objects (those which need to have a shadow from invisible character).
Set them as dummy and enable "Receive Shadows" in Dummy section. Those objects became *shadow catchers*. BTW, if there are only few objects, which receive a shadow, then you may choose not to duplicate them. You can always disable a dummy status.
You may want to use Shadow Casters to set shadows as your scene light shadows might not be enough to make is as dark as possible (you may tweak shadow later in in NLE).
For character, which needs to cast a shadow set all materials to PBR or Traditional (not DHS). Select all materials and set opacity to 1.
Render resulted scene normally.
In NLE compose clips and matte out the white for the second rendered clip (method depends on a type of NLE). Threshold should take care of that 1% opaque character.
Tweak further other parameters for shadow layer such as brightness, color, blur... etc.
There made one with this method