Those scores may not be the highest, but they are consistent, which is good.
You did absolutely the right thing in discussing whether to allow your son to take the tests on time with the Head, and the Head will need to confirm this in writing. It must be have been a difficult decision to make, with no crystal ball available!
Your mitigating circumstances are clearly going to carry a lot of weight with a panel. Although a panel would always tend to want to know "what went wrong on the actual days of the tests", I think it would be hard for them to demand specific reasons relating to just those two days in this situation.
The Head's support is going to be crucial to your appeal, especially the basis on which s/he decided upon a 1:1 ranking. Do you know where your son was on the Head's Order of Suitability? How many children above and below him passed?
I think the panel will also want to understand how your son has coped since returning to school. They will be looking for reassurance that he will be able to cope at a Grammar school, despite the disruption to his eduation.
You will need to find every scrap of academic evidence from before the accident to support your case. The high CATs scores and predicted Level 5 SATs are certainly going to help.
A panel would normally expect to see a child's most recent school books, and if they contain work of a high standard, that would be great. However, I am sure that a panel will also be very glad to see books from before the accident as part of the evidence.
I somehow don't think that your hearing is going to be the shortest this year.
So, my that's my two-pennorth worth for now - Capers123 is already circling, and I am sure the cavalry in the shape of the redoubtable Etienne will also be along soon.
Good luck, not just with your appeal, but to your son for a full recovery.