I think at the very least you should establish whether, once you have made your SD, the prosecutor is willing to do the deal. If not, obviously you needn't bother.
As for the rest. Most prosecutors are not bloodthirsty. Doing the plea deal (in normal circumstances) is never generally a problem and I believe there is only one instance on Pepipoo (which goes back a bit) where the deal was turned down. On that occasion the defendant was "less than polite" to the prosecutor, demanded this and that and told the prosecutor what he ought to do. So the prosecutor showed him and he ended up with nine points. In the main, provided they are sure you are not trying to evade your just deserts they simply want to see justice properly done.
I don't believe it will rest on what sort of day the Magistrate has had (and your case will probably be heard by a panel of three lay Magistrates rather than a District Judge alone). It is almost certainly a situation that they will not have encountered before and they will rely heavily on their Legal Advisor (who will probably be in the same position). So it should revert to what is "just."
IMHO, what is just is four lots of three points, a totting up ban (already served) and a licence free of points at the end of that ban. If you had heard about, and responded to each of these allegations in the usual way, that's exactly what would have happened. In fact, you would probably have been offered a course for one of them, but that's by the way. The complication is largely of your own making but an administrative oversight should not see an outcome that is so radically different to what would have occurred normally.
The fly in the ointment as I see it is that when you perform an SD, all the penalties and orders that were made as a result of the convictions you declare you were unaware of are set aside. That's fine when it comes to financial penalties and points - the money can be returned and the points removed from your record. But you served a ban as a result of those convictions and that cannot be reversed. That's why I believe a just solution should be found to take that into account.
I don't think there's much more I can add. Of course all this is only my own opinion, but it's the best I can offer.