Expand on your original points, remembering that the assessor will have no prior knowledge of the car park. Show us a draft before sending anything.
I'd be minded once you've appealed to file a complaint on the specific issue of their failure to offer a 40% discount.
Have you done this?
Can I use the fact they've given incorrect timings in my appeal too?
It's not, on the face of it, a reason why the charge is not owed, but I'd put it in there to highlight further evidence of their incompetence.
If you haven't yet complained to BPM about the discount issue, I would also add in a point around them misrepresenting the time allowed to appeal.