my real quandary is whether to go into this other stuff at all since it is hard to do in a snappy way
Very wise of you - I agree there's a risk of getting bogged down in too much unnecessary detail.
For extenuating circumstances, you need only write a single sentence mentioning grandfather, bullying, and mild dyslexia/dyspraxia. Take any evidence with you to the hearing, but leave it up to the panel to ask questions if they wish to know more. To be honest, with scores of 118/119 you don't need much in the way of extenuating circumstances.
My main concern is the extent of the academic evidence. You have one set of CATs, all of which are good. You don't have any more by chance?
I note the A for maths & science, but it can be difficult for a panel to interpret what that means. No doubt it's defined as 'excellent or 'very good', but one private school' s internal A grade could be another school's B ......
What are the comments like? Are there many references to high achievement?
I think we need to see exactly what the headteacher writes by way of support for the appeal.