Two months ago I changed around how the power supply works and completely forgot to document it here! Oooops. So, better late than never, here it is:
You can see a new bit of Veroboard with a couple of MOSFETs on to do the signalling, the red board is an 'ideal diode' module from eBay, and the blue board is a modified dc-dc converter module.
The net result is that the voltage regulation is now much better, and the NAS has been performing faultlessly ever since - despite numerous unexpected power cuts.