Well, a smidgeon of sympathy !! (lol)
I think in view of you rarely driving in Central London, it might be worth it submitting some representations, but this being TfL, don't expect them to roll-over. TfL seem to expect annybody in the whole of the UK to know the London CC intimately, even a bloke who's driven down from Wick to see his elderly mother before she passes away !
That is the law, unfortunately, and as we all know with zones like this, the law is an ass !
So submit reps and post-up their response here when you get it. Essentially, TfL's attitude is "Tough sh*t, we've heard it all before, so cough-up"