I'm testing a Pro815, dutifully bracketing +- 1 stop. I'm using default fine jpg.
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Using RAW, the next night, a waning gibbous, the results are a lot better:

The above image settings: ISO 50 f8 1/100.
I need to bracket much wider to see the limits... watch this space.
Does all the maths add up?
In the above images the zoom set to longest length - 420mm equiv. (104.7 true is stored in the image meta data.)
Moon image diameter in the above images is 346 pixels. Pixels across sensor 3264 (36mm equiv axis.)
Diameter on 36mm equiv sensor is 36 * 346 / 3264 = 3.816mm
tan A = opp / adj. = 1.908 / 420 = 0.004 = 0.26° * 2 = 0.52° (Which is about right!)
The camera's smallest aperture is f8.
The lunar f/11 rule says shutter speed is 1/ISO at f/11.
compare with Canon D30