Thanks for the thoughts. As you say, it might be worth exploring some of these ideas.
To be clear; Mazda have never insisted that I replace tyres with the identical original factory fitted type, only that I should have all four tyres of the same make and size. However, this is not always practical. In my case, I was stuck abroad, with a tyre which could not be repaired. An identical tyre was not available, so I had to opt for the nearest substitute. This was of exactly the same size, with a similar tread pattern, but from a different manufacturer. At a price of around £200, there is no way I could reasonably be expected to spend another £200 to replace it after returning home.
As you point out, after replacing a tyre (of the correct spec), all that should be required is a reset of the TPMS system, which should set a new baseline against which it can measure when pressure drops in one or more tyres. However, although I can reset the system easily enough, it will then trigger an alert quite randomly some time later. This appears to give the lie to Mazda's explanation, because if the 'mismatched' tyre is the cause of the alert being triggered, it should happen fairly quickly after a reset, which is not the case. The alarm may not appear for several hours into my next journey, or may even several days later. As I said, it seems completely random.
You mention the safety issues surrounding this fault. Whilst a reliable TPMS is very useful, an unreliable system is highly irritating and potentially dangerous, as it is a distraction and concern when driving.
Mazda have failed badly in this case; both in terms of the discourteous way they handled the conversation and also in refusing to acknowledge that there may be a fault with their system, proposing a completely crazy solution instead.
I have one further avenue to explore though. I have a family connection to one of Europe's senior car electronics troubleshooters, who has worked for several of the top manufacturers, tracking down the causes of faults like this. I'm going to tell him the story and see what he thinks.