Hi Ted,
Interesting. Glad to see that I understood the L curve in LAB space correctly. No need to apologize for the statistics, at least to me.
One question. You wrote this:
Then I applied a luminosity tone curve which was the same shape as that posted in the OP.
I don't know Raw therapee, so I don't know what you mean by a 'luminosity tone curve.' In photoshop, if you apply a tone curve without doing anything else, it applies the change to the color channels. You only get a luminosity-only curve by setting the blend mode to luminosity, rather than RGB, or by switching to LAB as you did. I'm assuming that the luminosity curve you are referring to is the garden-variety adjustment that acts on the color channels. Is that right?
Dan