Whilst your post rings true in some circumstances, many state grammars in the U.K. get the top grades in the country surpassing many independents.
I went to a super selective grammar school alongside my younger sister.
If I didn’t into the grammar school I would have ended up at boarding school to join my older sister. Two out of the three of us sailed into uni and maintained careers, one of us came out with OCD and failed her a levels, oh and smoking as well until my parents swiftly put a stop once she returned home.
I’ll let you guess which of us went to which school.
Educational consultant is best idea they can also help you secure a place in some of the harder to get into ones. Going to see the schools is essential. Despite the above, I went to see a boarding school recently for my dd as a backup for if she doesn’t pass the 11+ with an aim of transitioning from day school to full boarding by 13, I was blown away by it IRL compared to just researching them online. The facilities were definitely better than any grammar I’ve been to.
Not sure if this will help but where ever I’ve worked in the U.K. my school is recognised and getting a job has been pretty straightforward the minute I mention I went there. I suggest you seek schools with a similar effect if you’d rather pay for it. They will be blindingly obvious once you really get researching.
Well worth it IMO as has always given me great confidence when applying for anything. You clearly care for your dd education and many people do enjoy boarding. I was actual jealous of my dsis 