Apart from the alpha suggested above, which would require a proper UV, here's also an alternative using the selection tag itself as provided by the technical support.
The hidden polys command only hides them in the viewport, so if you render the viewport you'll see that the hidden polys are rendered (using the standard renderer). Same is true if you use the IRR. Since the Cycles RTP is in fact rendering the scene I don't think there's any way to not render those hidden polys.
The only way I can see to do it with the standard renderer is to use a material with an alpha channel set to pure black and restricted to the selection (scene attached). Then they will be invisible on render. Maybe you can do the same with Cycles.
Here's an example scene. It's animated with a Cycles mapping node, and relies on very specific UVs and gradient. Because of this, it's best to do this as a render pass and transition the object in compositing program. There are plenty of other ways to achieve this in C4D
Firstly I want to say that your explanation and research is great. I think you know more than me about cycles. But I recognize that sometime some fine-tune is easy than thinking complex. I deal with your issue with some fin- tune on mapping node and timeline.