I would also like to say that you wrote a great post Fraggle.
I have two comments to add, one supporting what you say, one disagreeing with you slightly.
My first comment is that the issues you are discussing are not the primary ones for Belleville/Honeywell obsessives. For many parents who would not consider High View or Falconbrook the issues are social. Quite simply, they want to be in a school where the large majority of parents are "people like them". And, speaking honestly, I can understand that, even if I don't agree with it. The nature of the SOME of the people who move to live BTC is because they want to be in a middle class ghetto (and there is nothing wrong with middle class ghettos) and it's not unexpected that they aren't keen on sending their children to school outside their comfort zone.
In my ways its like the parents who sent their children to independent school even though they don't believe it is better educationally than the good state (incl. grammar school) alternative - those parents do think that their children will make more useful contacts at independent school (e.g. if they go to Oxford or Cambridge or LSE or wherever the children will fit in better with the large number of students there who are the product of independent school.
Trying to get these parents to focus on educational outcomes of schools will not work, because these parents (correctly) recognise that test-based educational outcomes don't cover other things that schools impact on, like their child's accent (I'm not from London but I remember my mother being worried that I was picking up an inner-city accent at primary school - I was sent to public speaking classes straight away), the wealth/contacts of their child's friends' parents, the social activities of their child's classmates (e.g. skiing).
My second comment is that I would be a little wary of relying too much on the KS2 results data, in particular the breakdown of low attainers, middle attainers and high attainers. That categorisation is based on performance at KS1, so if children do badly at KS1 more of them will be classified as low attainers or middle attainers. Sometimes better grades for a particular cohort (low, middle or high) may reflect poor categorisation or poor results at KS1 level.