So... tempting fate by saying so, but ten days later, no recurrence.
I haven't yet cleaned the heatsinks or disturbed the system in any way whatsoever. Indoor climatic conditions have been similar, and system utilisation has been similar. The only change of any significance was a BIOS update, which included a CPU microcode. There was nothing in the release notes to suggest the microcode update would fix 'false' MCEs, but I guess it is possible. I've seen such things mentioned in other microcode updates for other CPUs.
Best I could get from reading Intel's processor documentation is that the MCE status decoded, in part, to 'internal timer error'. In my ignorance of Intel CPU internals, that tells me nothing useful. Whilst there are other bits in the status word that give further diagnostics, they seem to vary widely depending upon specific processor models, that I struggled to understand. And even if I'd succeeded in getting the further decode, most of the definitions were just as meaningless to me. I quickly found myself out of my depth in Intel jargon and decided to admit defeat.
One thing is, the machine is 5 years old. So, if there were an obscure CPU bug that depended upon a highly improbable coincidence of events within the CPU, and I eventually encountered it once after 5 years, I'd really need to wait another 20 or 30 years before claiming to have statistical evidence that it was fixed. In the absence of recurrence, I will try and remember to update this thread again around that time.