Respond to the SJPN by pleading not guilty to both offences. In the "reasons for pleading not guilty" section say you responded to the request for driver's details but still received nothing from the police. Go on to say you are willing to plead guilty to the speeding offence on the condition that the "failure to provide driver's details" charge is dropped. This is a common procedure which is well known to all court users (magistrates, their legal advisors and lawyers).
Before the pandemic it was necessary to attend court to negotiate this "deal". When the pandemic hit courts were obviously keen to avoid as many personal attendances as possible and arrangements were made for this deal to be accepted without a court attendance. Many courts have continued with this process so if you make your intentions clear in response to the SJPN you may be saved a trip.
You could also ask the court to consider sentencing you at the level equivalent to the fixed penalty (£100 and 3 points). Magistrates have guidance that suggests they should consider this in circumstances unconnected with the offence itself, such as administrative difficulties.
Wondering if this means I should plead guilty to the speeding and not guilty to the failure to provide driver details charge instead?
Absolutely not!You cannot be convicted of speeding unless you plead guilty as the police have no evidence that you were driving. This is your "leverage" to get the other (more serious) charge dropped.