There would seem to be 2 potential s. 172 defences. If the OP complied withe the substance of the legal requirements to accept the COFP - and with the level of detail provided by the OP regarding "the letter", this would be bound to fail, then I would argue that it would be an abuse of process to prosecute the OP for s. 172 - the purpose of s. 172 is to enable the driver to be identified and prosecuted for the speeding offence. Abuse of process would be an uphill struggle anyway, but in this case, just no. If the police "accepted" a verbal nomination over the phone, then no offence was committed, but if there was merely an administrative shortcut and the written response was still required, then not so much.
The other defence is so obvious that you'll be kicking yourself that you never saw it.
The OP will have been charged with failing to provide information between the issue date of "the letter" and the end of the period of 28 days beginning with the date of deemed service. If he takes along his witness and proves that the date of service was substantially later, the court will simply amend the information and convict.
So, he pleads not guilty and neglects to raise the issue of late service. He is convicted and appeals to the Crown Court. A Crown Court appeal is by way of re-hearing, so the court has no power to amend the charge, but (AFAIK) there is no restriction on adducing fresh evidence.
Simples.