MN, on the bullying data point, are the datasets 'matched' by school type and standard?
For example, you have said that it is the higher-performing schools that have remained girls only - so when the data on bullying is matched to similarly performing mixed and boys schools, is there still a clear difference in favour of girls schools? Or is reported bullying (or lack of it) a proxy measure of school performance?
Equally, are selective girls schools matched with selective co-ed and selective boys schools for the analysis of the data? Same for faith schools.
You see, if you said that high performing, private, selective and faith schools have slightly lower bulllying figures than the average for all other schools, that would seem to match a gut feeling that that would be what would be expected.
It is only if girls schools have less reported bullying that other schools of exactly the same type that the 'girlness' becames relevant IYSWIM?
I wonder whether there is also a reporting bias in that physical bullying (often, though not of course wholly, a 'male' thing) is reported and this shows up, while verbal / emotional bullying (the type at which, IME, girls most often take part in) is less often reported?