If you are convicted in your absence without being aware of the court proceedings against you, and make a statutory declaration within 21 days of becoming aware of the proceedings, the court must quash the conviction and basically reset proceedings to the service of the SJPN (albeit that they will ask for a plea there and then rather than you having 21 days to enter it online). In reality it is all but impossible to get an appointment to make a statutory declaration within 21 days, but as long as you contact the court within the 21 days to make an appointment, that is usually good enough.
As you were stopped at the time of the offence, and [presumably] warned that you might be prosecuted there was no requirement for a NIP. There was also no legal requirement to issue a COFP but they did and that was received.
Beyond the NIP/warning stage, nothing being sent to the "wrong" address creates a defence to the no insurance offence. Before you advised the police of your change of address, arguably nothing was their fault (not that fault is relevant here). Subsequently, the police seem to have made a right horlicks of matters, but as mentioned above, that is of limited assistance.
Where the police making a horlicks of things potentially comes into play is if you do/did not make a statutory declaration within the 21 days. Outwith the 21 days the court have the discretion to quash the conviction if the consider that it was in the interests of justice to do so. If you simply could not be bothered, then they would be unlikely to find it in the interests of justice. If you have been proactive and the system has let you down, then it would seem harder to refuse.
The overarching principle is that the right to a fair trial requires that you have the opportunity to defend the charges, or otherwise have your say. Within the 21 days it matters not why you were not aware of the proceedings - whether you simply didn't bother to read your post or whether the police sent it to an entirely random address. Beyond the 21 days, everything matters - the court have the discretion in the interests of justice, rather than being bound by law.
Off the top of my head, £660 is the standard fine for the offence, based on a Relevant Weekly Income of £440, and no discount as there was no guilty plea. On top of this there would generally be a 40% surcharge and ~£95 prosecution costs.
On conviction, the court is required to endorse your licence with 6-8 points or ban you outright. Absent any aggravating factors, I would have expected 6 points.
If the case is re-opened (quashed and re-started), you should be entitled to a 1/3 discount if you plead guilty at the earliest opportunity, and you could ask the court to consider sentencing you at the fixed penalty level - as you were unable to accept a fixed penalty for reasons unconnected with the offence. Whether the court will decline on the basis that it's you own fault for not reading the form properly might depend on how much sympathy they feel for you having been given the run-around by the system.
