Furthermore, their assertion that my car was parked "in a manner consistent with double parking" would surely require there to be another vehicle between my car and the kerb?
Is irrelevant as regards consideration of the legal issues IMO.
Just because they want to commit to this nonsense doesn't require you to rebut in detail.
Pl post the rest of the NOR i.e. everything up to and including the signature: this part is procedurally the most important.