Thanks for the background information, and I'm so sorry to hear how difficult things have been.
In answer to your first question, I feel sure it would not be legally possible. I think all evidence would have to be disclosed, and open to discussion, at the hearing. If you'd like to ring the Appeals team, they will give you an authoritative answer, consulting their own solicitor if necessary. I don't know if they can suggest any way round your basic problem - I'm afraid I'm not aware of one, although there must have been one or two cases not dissimilar in the past.
I would make just one observation about the academic evidence. With such low scores, as you realise, the panel is going to need a lot of convincing - irrespective of curriculum-based evidence and any extenuating circumstances.
In my view, to stand a chance, you would need compelling alternative evidence of reasoning ability (e.g. CAT or NFER VR scores from school, or WISC/BAS test results from an educational psychologist). By 'compelling', I'm thinking of something around the 95th percentile!
Wish I could be of more help - please come back if you have any further questions.