Thank you SO much, everyone, for these insights: I'm really grateful to you all for taking the time to respond, and all of this is enormously valuable - so hard to find out in other ways.
To answer @Treehouse12 , no - DD is in a state primary and we were thinking she'd just continue to a state secondary, but we weren't offered any of our preference schools (including catchment) so did an emergency volte face and tried to find a place at a local private school after offer day in March. Which means we (and she) have seen very few schools, and are basically clueless; probably beta or even gamma parents, if I'm honest, very much joining @gizmo in the windswept cyclist corner.
@weepurpleybird Your account is really interesting; thank you for being so honest. If we put DD forward and she gets a place she won't have had any tutoring - the test is next week (and @bimblebird you must surely be right about the ratio of desperate parents to places!). I do worry about her being out of place, or feeling pressured; as people have said, I'm sure that could happen anywhere, and we as parents will have to do everything we can to manage expectations and make sure we keep up the support. @PeonyBlush10 I work in higher education and I recognise this exactly: family pressure, or even pressure from the student themselves, causing more issues than the expectations of the institution. DD's happiness is, frankly, all I really care about, and I'm sure that's true of basically everyone; but she does need to develop a little resilience, and better grades will give her more choice later on.
It's clearly a wonderful school on a beautiful site; @Treehouse12 and@Nenen , you've exactly hit it: my main worry about the Stephen Perse is how confined it all feels, though I suppose the botanic garden is a hop and a skip away. Nothing like having your own trees, however.
All of it feels a bit overwhelming, not least the financial side - it's affordable but not easily, so I really don't want to mess up the decision. But oddly enough, the thought that it's likely to be very competitive is weirdly encouraging, in a sort of lap-of-fate way - I think we'll give it a shot!