I haven't seen the traffic order but I very much doubt that it specifies payment in detail because if it did then an amendment, with all the consultation faff which is required, would be needed whenever details were changed.
The PCN wan't issued because you paid for the wrong location, it was issued because the only available source of info available to the CEO showed that a payment corresponding to this unlawful parking place had not been made.
OP, don't overthink this by overlaying with what you know and then thinking that the CEO knew the same, because they didn't.
As suggested , simple reps.
Surprised and couldn't understand why; had to recheck my payment and time in bay and then realised that instead of location 6336 I had input 6366. However, payment of the correct tariff for the period parked was made - 6366 is also a payment location within the borough of Barnet- and therefore the correct payment amount was made in respect of my vehicle VRM ****.
Attach whatever proves the above e.g. the tariffs for both locations, payment receipt, perhaps something from your bank/credit card account and copy of your V5C etc. These show the link between the person submitting the reps, the vehicle and payment.
I suggest putting a draft here first.