This is one where Birmingham ought to use their discretion to cancel being as you did pay and simply made a silly error. No intend to avoid or gain from a wrong click.
However, as said, Birmingham are playing hardball and not re-offering discount if/when they reject.
So asking for discretion would be risking the full amount.
The plus side to Birmingham's policy seems to be that more people are taking it to tribunal after having had representations rejected, after all there is nothing to lose by doing so and Birmingham could be struggling to cope, they do seem to be not contesting many.
If it did go to appeal, IMO an adjudicator could go either way.
They cannot find on discretion but can decide that Birmingham failed to consider discretion.
Could also find that the date error was immaterial and that you had paid.
Or that the date was critical so full penalty is due.
Your money, your risk, I'd say a little better on 50/50 to win and I would risk the extra 60.
But it isn't guaranteed
