On what you have shown so far, your best point is not really that the council were slow and awkward, although they plainly were, but whether the actual Notice of Rejection is legally defective, because if it misstated your appeal rights, the late-appeal position, or the council's power to increase the penalty, that is procedural impropriety and is a proper appeal point rather than just a fairness complaint.
If the documents do not prove that sort of defect, your next best course is to put in a short, tidy chronology with the key permit emails and explain that you were trying to renew, the same vehicle appears to have been treated inconsistently across permit years, and you bought the higher permit once the matter became impossible, but you should be realistic that this is more a discretion argument than a knockout legal defence.
So the practical answer is simple: get the actual documents in order, rely on any defect in the Notice of Rejection if it is there, attend the Teams hearing, and keep your explanation calm and factual, because adjudicators decide cases on evidence not indignation, however richly the council may have earned it.
