I'd keep this nice and simple, as we know the council will likely reject no matter what you say:
Dear Portsmouth City Council,
I challenge liability on the ground that the alleged contravention did not occur, and also that the amount demanded on the face of the penalty charge exceeds the amount due by law. Nothing in regulation 7 of The Road User Charging Schemes (Penalty Charges, Adjudication and Enforcement) (England) Regulations 2013 permits the council to demand payment of the CAZ charge in addition to the penalty, the only amount that may be demanded is £120, discounted to £60 if paid during the 14 day discount period. There is no statutory authority to demand £170 discounted to £110 if paid during the 14 day discount period.
It follows that the penalty charge must be cancelled.
Yours faithfully,
You don't want to say anything about signage because you cannot do so without making some self-incriminating admission or another, so you might as well wait and see what evidence of signage they can come up with first.
Make the representations online and make sure to keep a screenshot of the confirmation page.