The new image I mentioned above makes it clear to me that there are (at least) two overlapping diffraction patterns.
The primary pattern involves a reflection off the inside surface of the sensor cover glass located a fraction of a millimetre above the sensor surface. The second pattern involves a longer light path and is probably caused by
A double refection between the sensor and the inside surface of the cover glass
or more likely:
A reflection off the outer surface of the cover glass i.e. light that is not reflected back by inner surface enters the glass and is subject to an internal reflection within the cover glass - back towards the sensor.
This would account for why we observe large discs overlapping smaller discs in the diffraction pattern.