How can you make backfaces render based off what the camera can see?

I have a scene where I’m using a geometry node’s backfaces input to mix two shaders. I like the fact that the camera can only see the inside walls of my object (as it is only rendering backwards normals), but there are a few issues.

I would like the front-facing normals that the camera can’t see to be rendered, and the backwards facing normals of faces the camera can see to not be rendered (as they influence other objects). I have rerouted all rays except the camera rays from before the front faces are cut-out and frankensteined them back on to only the camera rays of the image after the operation so that I can preserve the caustics coming from the correct area.

nodes

The main problem I need to solve now is the fact that the backfaces of the faces closest to the camera are rendering and casting a shadow and reflection on the object in the center of the cube.

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The red arrows in the second pic show the light coming from the part the camera can’t see reflect on the center object. The blue arrows show what actually creates the reflection of the cube sense the backfaces of what the camera CAN see are transparent. Although in the image, the bottom of the cube is being reflected due to my node work-around. I still would like to make it so the backfaces of the faces being deemed transparent to the camera to not render. Any help is appreciated!