Same issue essentially. Calibration, or 3D LUT calibration expects a stable display/image characteristic to which it will correct towards. If thats not there - it breaks calibration as a concept.
I have a similar issue with my 2016 LG OLED, which has dynamic dimming based on the average brightness level of the image (so had plasma TVs in the past (less aggressively)) - there is no way to correct that with normal calibration, or 3D LUTs.
But - the "feature" here at least gets disabled, once you put 10% color windows on screen for calibration - so you are calibrating a stable display state - and the deviation (in brightness) only then sets in (based on the scenes average brightness level (if it gets too high)) afterwards.
As this "dynamic adjustment" only is present in maybe 2% of the scenes in an average movie calibration still makes sense though. (I also have a 3D LUT box, and I can do jack about it - so I'm speaking from practical experience.
If you've got a "dynamic adjustment" based on roomlight f.e. (as lets say a Macbook with an ambient light sensor has), the measured gamma (SDR) varies by a significant amount even while measuring a 10 step grayscale. So you absolutely have to disable that (which you can on a Macbook) before even attempting to calibrate (or profile the display).
A 3D Lut is basically a correction based on 1000s of individual measurements and not 10 as in the example above, so it amplifies the problem.
You have to understand, that what a 3D Lut does is, that it moves individual color points 'more' than f.e. just a normal greyscale (whitepoint) and CMS (primary colors at 100% saturation) calibration. And it does so not in one direction (vector) but in thousands.
And your fundamental problem with "dynamic brightness adjustment" is, that one and the same color, will be displayed differently based on roomlight, or average picture brightness level (didn't read up on your projector and what it does). So the same color gets displayed different based on criteria you dont control.
You absolutely cant calibrate this away. (Think about it for a minute..
In closing - again, most displays/projectors that use a form of dynamic brightness adjustment (if its based on average image brightness level), will disable it, when you calibrate with 10% windows (size of the calibration pattern), or 10% windows with APL (average picture level) compensation (basically if bright window, make boarder dark, if dark window make border brighter (grey) - so average image level doesnt fluctuate as much). And then you can calibrate.
But if you see gamma curving away from target at the lower end - always even in your default 'cinema modes' presets, on an SDR calibration - it likely means, that dynamic brightness adjustment is impacting your calibration - and thereby ruining it. And deviations from target would be visible at 20% and 30% grey as well. (Not just 10% where gamma can break depending on display characteristic alone.)
If your gamma is on target - meaning, following it roughly (like you've posted in the last graph) - it means, that at least during calibration "dynamic brightness adjustment" is disabled. Which means, you can calibrate (or even 3D LUT calibrate) the thing on a base level (then ignore the error that sets in, when dynamic brightness adjustment sets in on real life content).
Basically calibration, or 3D LUT calibration doesnt deal with a temporal (time as a dimension
) element. It wants and needs stable readings throughout the process.