You also need to be aware that proving academic ability is the easy (relatively) part.
I wouldn't go quite that far.
Many parents struggle to prove academic ability, perhaps because their school isn't very good at wording its support.
Some state school heads are opposed to selection and won't co-operate fully.
At the other extreme, some heads exaggerate their support to the point where it becomes unrealistic and devalued!
You will also need to convince each appeal committee why your child's need
For a Place at the school is greater than the detriment caused to the school by admitting over PAN (assuming that the school is full). These reasons will probably be different for each school and need to be specific to that school, and not just "my child would flourish with a grammar school education"
I strongly agree. I get the impression many parents spend too little time on this, resorting to generalities and platitudes ("He needs to be stretched