You passed the usual "Flying motorbike" signs; they are visible in your photo, and seem pretty clear on the approach to them. So I don't think any representations based on inadequate signing are a runner. Having said that, photos of the signs taken as an approaching motorist sees t hem would be useful.
On the face of it, and reading your narrative, you would seem to have only the mitigating grounds you have described. However, that's not the end of the story, because this restriction is based on a traffic regulation order, which may contain something that permits emergency entry at the restricted times. Our adminstrator can probably obtain the TRO to see whether there is any get-out like this in it. However, there is a limited time period in which to submit representations, so it would be best for you to submit representations based on your urgent needs as per your narrative. Council parking department officials do seem to have hearts of stone, however, and have "heard it all before", so you would need to back up your reps with whatever medical evidence you may have,and include copies in with your reps.