Shadows from culled objects

I have a character in the scene with his own orbiting camera, which is culling everything except him. This camera's output is then being used in a RenderTexture to create a Sprite effect of sorts elsewhere.

The problem is, since I'm culling the rest of the scene from this camera view, I don't see any of the shadows from the nearby environment on the character.

I fear I may have given myself an unsolvable problem here. Is there any way to have culled objects still cast shadows? (Material effects probably wont work, as these same shadows-casting meshes need to be visible to other cameras in the scene).

Thanks!