I have continued work on this. I now have a figure with the inner and outer spheres joined. It's no longer possible to ruin the alignment by grabbing the inner sphere and moving it.

I have added a separate parameter value for the environment Reflection versus the Indirect Diffuse Lighting reflection. They are actually coupled but I managed to decouple them a bit.

Here I'm starting with everything neutral.

Now I decrease the IDL value to -2 stops - I get less ambient light but the reflections are the same.

Or, I can increase the Reflections by 2 stops while keeping the ambient lighting the same.

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Renderosity forum reply notifications are wonky. If I read a follow-up in a thread, but I don't myself reply, then notifications no longer happen AT ALL on that thread. So if I seem to be ignoring a question, that's why. (Updated September 23, 2019)