IMO, if you are adamant that you did not pass the required CPZ gateway signs on your route to the location and you want to present this then do so. As far as I know you cannot prove this, it's your assertion, but it's one which you made in your reps and which has been ignored in the NOR which instead goes on at length with a cut-and-paste recitation of the purpose of CPZs and how they should be signed. It appears that the authority haven't presented evidence for the adjudicator either.
There's a further procedural impropriety in the NOR in that contrary to regulations the authority did not advise you that, subject to conditions, you could apply to the adjudicator to register an appeal after the expiry of the 28-day period*. In fact the NOR reinforces this as an absolute limit by stating that once they have served a Charge Certificate 'you would have missed the opportunity to appeal'.
As I understand it, the adjudicator's power in this regard is not subject to whim of the authority's administrative processes.
And it's the authority's evidence that Athlone's NTO was cancelled on the grounds that they were a hire company and the car was subject to a hiring agreement.
And you've now reinforced the point that you did not hire the car, your insurer did.
* 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,
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.