So, an update. In the end I did manage to speak to someone at Apple who - while still not acknowledging that Apple is aware of any issue - was empathic and helpful, and arranged for me to send the faulty HomePod in for service... and a replacement HomePod has now been sent to me which I received yesterday.
I've set it up - in a stereo pair with the other one I had, which hasn't (yet) had any issues - and all good for now. I've resisted the prompted software update (ie they're both still on 26.5) for now, for obvious reasons. I don't have a high level of confidence about how long these will last before the ghost touch issues return, but for now I'm happy with this outcome.
I guess my advice would be (for whatever it's worth): be kind but be persistent, and hopefully Apple will do the right thing in the end.