If Etienne or anyone else in the know reads my thread and thinks score of 281 is prohibitively low, please let me know as don't want to waste time on a lost cause. http://www.elevenplusexams.co.uk/appeals/general#a36
He is happy with secondary offer and understands that an appeal would prob be unsuccessful, but is still adamant he wants to try.
That seems to me a very reasonable approach.
The advice I usually give is "no matter how good a case you may have, it is very unwise to go into an appeal expecting to win. Hope for the best, but be prepared for the worst.
Appeals tend to be unpredictable - you can never be entirely sure what might happen.
There appear to be exceptional reasons for underperformance on the day - to counterbalance that underperformance you need as much academic evidence as possible to convince the panel of his very high ability. Focus on that, and let the medical evidence simply speak for itself.