If anyone's interested, the new CPS cured the problem - as expected.
I found a new Facet replacement on Ebay for £30 delivered, which was a good deal better than the £80-odd from just about everywhere else. GSF refunded the payment immediately for the incorrect part, so they get a thumbs up from me.
I fitted it in under 15 minutes, including getting the car up on stands and then back down again afterwards. I don't know if all 147 TSs are the same, but I would definitely advocate doing this job from underneath. No need to remove anything - not even lifting the bonnet - as you can see the CPS from underneath and access is actually OK. Like I said - sub-15 minute job in the end.