The offence that you have been charged with is speeding, not failing to comply with the requirements of the COFP.
They received your s. 172 response admitting to being the driver, which enabled them to issue a COFP (not an FPN).
You were offered an out of court disposal, which they claim you did not comply with the requirements to accept. If you could prove that you complied, then the prosecution would be unlawful, but being fairly sure that you sent it with nothing to support your vague recollection isn't going to cut it.
As regards your guilt or otherwise of the alleged speeding offence, an unaccepted out of court disposal offer is neither here nor there. Assuming that you have no viable defence, the relevance of the COFP is that the Mags' sentencing guidance says to consider sentencing equivalent to the fixed penalty level where a fixed penalty could not be accepted for reasons unconnected with the offence - so broadly if a fixed penalty would normally have been offered.
It will be entirely within the gift of the court to decide either that it's your own fault for not reading the form properly and sentence you in line with the general guidance, or that the absurd number of such cases coming before them is due to an unduly convoluted process and/or poorly designed form and sentence you equivalently to the fixed penalty. If you ask them to consider doing so.
Evidence of a diagnosed mental illness which contributed to the failure to comply with the requirements might reduce the chances of the bench deciding that it's all your own fault. However, with any mitigation concerning diminished capacity (mental or physical), it is prudent to consider whether the bench might question whether or not you ought to be driving at all. The fact that you have been diagnosed by a doctor who (presumably) has not decided that your condition is reportable to the DVLA, would suggest that this ought not to be a major issue in your case.