The requirement (that we can confidently assume that you and many, many others failed to comply with) is, in law at least, to provide your name, date of birth and driving licence number, to the relevant person (fixed penalty clerk) (s. 75(8A) Road Traffic Offenders Act 1988).
There has been no requirement to send your physical licence off to accept a COFP for some time now, so the fact that you were in the US and therefore somehow unable to send it off (presumably the US does not have a postal service?) is irrelevant as that was not a [legal] requirement.
Assuming that you failed to separately provide the required information (or any requirements that the police might decided to unlawfully seek to impose), but that in order to make payment of the fixed penalty to the relevant person (fixed penalty clerk) you provided your name and UK licence number (UK licence number incorporates date of birth), I would argue that you had complied with the legal requirements and that the subsequent proceedings were unlawful.
If the above applies, I would suggest that that would be your route of challenge. If you had not substantively provided your date of birth, then it would appear that you had not complied with the requirements.
There is provision in the Magistrates' Sentencing Guidelines for imposing a penalty equivalent to the fixed penalty in circumstances where a fixed penalty could not be taken up for reasons unconnected with the offence. When raised in the mitigation section, this appears to be regularly ignored by the SJPN process, or alternatively, according to our resident gobshite, if you hadn't made a "poor" submission you would have gotten a lighter sentence.