Well, I seem to be out of the woods.
Initial replacement of the power supply (was not my idea), followed by the main logic board (yay!) and incidentally the hard drive cable - which got damaged during the previous surgeries.
I got the machine back after 10 days, and the symptoms had worsened - 5 hard power offs (no warning, no freeze) during the first 7 days after I got it back.
So back it went for a third Genius Bar investigation/disassembly over another week, where no fault was found. At that point I was very VERY annoyed, as there was a total refusal to replace the machine under warranty, and all attempts to get a replacement under consumer rights law (as the machine was not of sufficient quality) were refused also.
So I took the machine back and tried to get the Online Store to replace it, as the Retail Store seemingly operate totally separately and can't replace units that were built to order - only the stock builds they sell themselves? Bizarre. Apple is Apple to me. Why is their internal stock control my problem?
So, all was well for 9 more days, then I had another unscheduled hard power off. Having exhausted all avenues to get Apple to take it back, I decided all I could do was a complete "nuke and pave".
So I reformatted the internal drive completely, and installed Sierra as a factory-fresh install. I then *avoided* Migration Assistant and instead recovered my documents *only* by copying from a mounted Time Machine backup. (And then recovering the data for applications that store content in ~/Library/Containers rather than ~/Documents!)
All applications were reinstalled from the App Store / fresh downloads.
So far (touch wood) it's been nearly 4 weeks without another hang / power off. The fact that the machine powered off hard after the MLB replacement makes me believe that actually the largest contribution to stability might be the fresh installation of Sierra. It's possible that something wasn't adequately reconnected after the MLB replacement, was improved in the next visit (thus only one power off) and finally resolved by the Sierra update, but this has been horrific to debug and my heart goes out to the Apple engineers (hardware and software) who have no doubt been working on this behind the scenes.
Apple's reputation for customer service excellence is in tatters for me - because of some appalling communications failures/repeatedly broken promises that made a bad problem worse and basically left me with the impression I was assumed to be lying. Replacing the hardware components under warranty was touted as a "goodwill gesture", but the obstinacy in not replacing the machine which continued to fail after point that seemed arrogant and unreasonable.
Apple refused to release transcripts of my service desk cases to support a complaint in writing / application to the Consumer Rights ombudsman, unless I applied to Apple Legal, which seems designed to impede such course. And they succeeded, because I've lost the energy to do so, regardless of the outcome.
I think this *should* be exposed as a disaster of customer service but frankly would rather put my efforts into something else.
My formal complaint at the end of the process was not followed up and no kind of compensation was offered for the 6 months of phone calls, multiple visits to the Genius Bar etc. Not even an iTunes gift card.
I tell everyone I use Macs because they annoy me less than Windows machines, and stay out of my face. That belief is very severely dented now. I hope Sierra lives up to its marketing, and I can get back to enjoying using my iMac again.