@after8itsgrownuptime With 11+ pressure I think its all about choosing the right schools to go for. My DS2 did his in January and while it was stressful for me, he sailed through it and had little pressure. I choose schools carefully that I knew he would get places in, one stretch, one certainty and two (yes two) backups. He even then he only got two places (the certainty and one backup).
Another parent I met recently was upset that her son hadn't got any places, when I talked to her - genuinely trying to help, it turned out she had gone for what I would describe as 3 super stretch schools and one stretch for her child...."He's a bright boy and I thought he'd get one of them". When I started suggesting other schools, I got lots of "oh I couldn't send him there" and no realism at all!! Her current plan is back to prep for 2 more years to try it all again as "he's not quite ready..."
The moral of this story is to not try to overthink the 11+, and basically put her in for every exam she's likely to get - Girls schools I know less well, but I think you are looking at St Catherine's, HCH, Radnor + one stretch.
I'd get her into a good local prep and take the schools/heads advice on where to sit her.... and really do put in at least 2 backups!!
I think if she's not super bright and you want her in private you may have to forget about "choosing" a school - Independents in this area are not a buyers market - there are too few places for pupils, and you may have to accept that some schools while they may not appear perfect may be ultimately right for your dc.
I also think it's a bit of a myth looking "to avoid the 11+" most schools will select to a degree at any entry point, Radnor currently are less selective at y5, and miss the 11+ but that will change very soon as they are getting very popular at 11+... Claremont for example, although they are a 3-18 school, select at 11, and its not a certainty to progress from the prep to the senior school.
I hope you get what I'm saying here! I started this journey in much the same way as you looking for the "perfect" school for my DS1, it was a bit of a shock to realise you don't really have a choice, only a minority of super bright kids get to properly "choose" their school.