Little update from me. I reviewed the product on Amazon, pointing out very clearly (ahem!) that the flowchart diagram is wrong. I was then contacted by the UK seller (Wankaku) to tell me that, no, the diagram is correct - the camera WILL return from auto shutdown on a g-shock. When I protested, they contacted the manufacturer, who confirmed that, yes, that is the way it is SUPPOSED to work (wakes up from auto shutdown with a g-shock as in the diagram) BUT that they have had other reports of this not working properly!
So it seems that the camera is SUPPOSED to work per the diagram, but in practice it does not. The good news is that the manufacturer has indicated that they may be able to fix the problem via a software update. How long that will take to become available I don't know, but I will keep chasing the UK vendor to get this fixed. The UK vendor (Wankaku) are extremely responsive and eager to help, so I have some optimism that this MIGHT get fixed.