IMO, you have two separate issues here:
1. Their evidence that they considered and rejected your formal representations and your claim that you did not receive this response. This is procedural and financial;
2. The substantive matter of your PCN and whether an adjudicator would allow any appeal, which also has financial implications.
As regards 1, we will guide you in order to reduce the current charge of £240 down to at least £120 and possibly £60.
As regards 2, we would advise how to take the matter to adjudication and give views on your prospects.
For now there is nothing for you to do. You do not step outside procedure with correspondence to all and sundry, you stay within procedure, keep an eye on your post and the council's website once the CC's 14 days have expired and keep us up to speed.