From my exerience of contesting a penalty served by APCOA, my advice is: should you appeal to adjudication and the decisions are negative, then appeal again to the 'Cheif Adjudicator'.
In my particular expereince I argued at length my case in the first instance and then after the first negative decsion I argued against the reasoning behind their decision. After another round of negative decisions I appealed to the cheif adjudicator.
They're inclined to give a negative decison in the first instance at least. Its probably a matter of course. So if you're are on higher ground, which you are, then don't take their initial decisions as real contemplative decisions - appeal to the cheif adjudicator, even though they may say there's no further appeal in their decision letters. He/She has more power to undo the rigid net of law that has caught the wrong fish. He/She is most open to making a fair decsion. Give him/her an amalgamtion of what you put to the standard adjudicators and maybe your penalty will be waived like mine.
Like most advice on here, it's matter of convincing them you're for real. Tenacity is key.