I just want to bump this thread and mention that we did not find a solution yet, but when we do, we will definitely share it with everyone in an update.
The view port idea worked in theory, but the workflow behind it was very cumbersome for us and our workflow.
However, we did find a shader that kinda works. I just want to point out that shaders are way beyond our expertise, might as well be black magic.
The shader in question (link) adds more blending modes to Godot, and it turns out that the "add" blend mode does achieve the effect we are looking for, to an extent. Here is how the implementation looks in Godot.

And here is how it looks when it is working:

As you can see, the shadow of the two separate scenes blend in together correctly.
However, the effect breaks if the character/camera is parallel to the objects, for some reason. Like this

We are still investigating why this happens. Does anyone have any idea?