Have you tried Plan A? Get in touch with the management at the cinema and ask them to get the PCN cancelled.
In your comms with the PPC, you are almost giving away that you're probably the driver which is a pity as, whilst the NtK purports to be PoFA compliant, it has failed to include PoFA 9(2)(e)(i) which, in effect, nullifies EPCs right to transfer liability from the driver to the keeper.
Why are you even communicating with the ECP? Whilst it may be too late, your Plan B appeal as the "keeper" can be made on their website. You point out that you registered your vehicle at the cinema, you have proof of being a patron, their NtK fails PoFA on 9(2)(e)(i) and so you, as the keeper, are not liable, the signage at that car park is not adequate enough to bring to the attention of the driver the charge which is another failure of PoFA 2(3)(b)(ii).
When they reject your appeal (highly likely) then you move on to Plan C which is an appeal to POPLA. POPLA will only consider breaches of the BPA CoP and relevant law to ascertain whether the PCN was issued correctly. No mitigating circumstances are considered. You have to lead the POPLA assessor to your points. In this case, unless you can show that there is a clause in the terms on the signs at the site about registering at the cinema for extended stay, they will consider the PCN was issued correctly.
ECP tend not to be particularly litigious and if they do proceed that far, it tends to be in the hope you are low hanging fruit on the gullible tree and will capitulate and fund their scam once the debt collector letters and the threat of court action begins. Debt collector letters are safely ignored as they are simply designed to scare you into paying. The debt collector has no skin in the game and cannot bring any action against the keeper.
QDR are not acting as solicitors but just another arm of the debt collection service. Unless you receive a Letter of Claim, which must give you a minimum of 30 days to respond (ignore anything that pretends to be a letter of claim that only gives you 14 days to respond) you can ignore it.
Plan D is the best option as it gives you the best chance of getting this cancelled. A judge is the only truly independent arbiter and would decide whether you owe ECP a debt or not. ECP tend not to want to progress it as far as this as they know they are on thin ice with a claim.
One thing you MUST do immediately, is send a data rectification notice to ECPs DPO. You must instruct them to rectify your address for service and to erase your old address. The debt collector has done a simple credit search to find your current address. However, leaving them with two possible addresses is a sure way to get a CCJ by default. You should also update your V5C address online with the DVLA.
Whilst it is your responsibility to keep your V5C address up to date, it is often overlooked. You can send a "complaint", not an "appeal" to ECP telling them the origin NtK was never served at your current address and that they should now send you a new NtK at your correct address and start the clock again. They'll probably tell you to go and sod off. However, you point out that the BPA CoP clause 23.8 requires them to consider appeals outside of the 28 day period for exceptional circumstances why the appeal was not lodged in time. In your case, the NtK was not served to your correct address. If they refuse, you then complain about this to the BPA.