Well, after all that messing about on Monday evening, the car was locked with the key and left to sit in our multistory car park until it was time for me to go home on yesterday (Thursday) afternoon, ready to take to the dealers this morning.
I unlocked it with the key-fob threw my stuff in and was about to drive off but, I thought let's give it one more try ...
Lock car with key-fob button - One Flash of indicators... nothing else, no additional 3 to indicate any disarming of sensors.

Maybe? Decide to initiate alarm condition by opening with key. It alarmed!

Lights flashed everything! It even cancelled when I pressed the button!

Will it work if I leave a window open? Leans in window ...

Yes! Again everything worked fine!
I'm wondering if doing all the reset stuff and leaving it for a while allowed it to re-sync itself somehow?
Anyway, it's Friday morning and it hasn't gone off on its own at all overnight. I've cancelled taking it to Arnold Clark because they not only charge
£15 for Courtesy Car insurance but, they also charge
£20 for any Warranty investigations that fail to turn up anything! Bawz to that, I'm not taking it in to be charged for nothing. I'm still waiting for the £15 cheque after they charged me twice for their 5 day drive-away insurance..
We'll see how it goes over the next few weeks. It's got a 3 year warranty after all!

-LaZ-