Looks like some mendacity on the part of the CEO re tyre valve positions ! However it does look as if they treat all the separate bays that come under St John's Green as one area for parking, with identical restrictions, so moving from one bay to another does not trump the 2 hour limit.
Clearly your informal challenge has been rejected, so the next stage is the Notice to Owner, where you can submit a formal representations.
All you can do at the NtO stage is state the facts; that you moved the car before the 2 hours was up, and re-parked elsewhere in St Johns Green in a totally separate bay. You might not get away with this because the TRO lists the relevant bays under one single location, so the contravention is, in theory, made out. I think your wifes "clever wheeze" to thwart the 2 hour rule may not be valid. Certainly the council are unlikely to give way, so you'd have to take them to the Traffic Penalty Tribunal. The discount option is lost at the Notice to Owner stage, by the way.
The other aspect is the PCN itself and its content. We often find fatal errors in PCN that on their own, win appeals even if the contravention is made out. This is because a learned judge, some years ago stated that, (for parking PCN penalties), that a penalty can be demanded if a set of statutory conditions exists. An error on a PCN can be such that it is a procedural impropriety and thus the PCN is void.
So please post-up all of the PCN, top to bottom and all sides.