Some thoughts.
The photo of the PPA signs which you posted - after returning to take photos - and theirs are not the same.
Is your evidence valid, because this is how you entered the area, or is theirs?
We don't know, but IMO it's important. Which is it?
They have not offered the reduced sum, which IMO is grounds on its own for appealing because their reasoning has totally changed i.e. CPZ with informal reps and PPA and no re-offer of lower sum with NOR.
And the NOR does not inform you of your correct rights of appeal:
The regs provide:
(6) If the enforcement authority does not accept the representations, its decision notice—
(a)must—
(i)state that a charge certificate may be served on the recipient unless within the period of 28 days beginning with the date of service of the decision notice—
(aa)the penalty charge is paid, or
(bb)the recipient appeals to an adjudicator against the penalty charge,
(ii)indicate the nature of an adjudicator’s power to award costs, and
(iii)describe the form and manner in which an appeal to an adjudicator must be made
The highlighted part is itself in 2 parts, BOTH of which IMO are of equal importance in conveying an appellant's rights:
Appeal to an adjudicator against a decision to reject a recipient’s representations
7.—(1) A recipient may appeal to an adjudicator against an enforcement authority’s decision not to accept their representations.
(2) An appeal under this regulation must be made within—
(a)the period of 28 days beginning with the date of service of the decision notice under regulation 6(4)(b) which states that the enforcement authority does not accept the recipient’s representations, or
(b)such longer period as the adjudicator may allow.
The highlighted part is not in the decision notice(AKA NOR).
Perhaps they'll try and finesse this by saying that it's in the 'enclosed Notice of Appeal form', in which you will find oblique reference in the small print. But IMO, this form does not relieve the authority of its obligation to include this within its notice. And if they say that the 'enclosed appeal form' counts as part of the notice, then this is grounds on its own because the form states clearly that 'you have 28 days from receiving the ...Notice of Rejection.' in which to appeal.
These might be the internal standards of the adjudicators, but it is NOT the position in law i.e. your legal right to have a valid appeal registered(irrespective of the adjudicators)is the 28-day period beginning on the deemed date of service which, unless the contrary is proved, is 2 working days after posting. The adjudicators' power to accept a late appeal ONLY commences once it's late! Which means that in-time and options if late must be included within a NOR.
But they're not.
Contravention did not occur;
Procedural impropriety.