Unfortunately yes, being put into the Pathway for assessment can be very, very influenced by the School avd if you have a Dd who masks at school and attains grades but meltdown when they get home it will be very, very difficult to get a referral. In my opinion, and it is just that, the referral process still very much favours boys who often mask less at school.
I would start by doing this very simple progress checker. If it says they she needs some support they will send you some links to resources and you can book an appointment with one if their SaLTs, although it is a Charity so you might want to make a donation.
You can show the GP the results, if it says she needs support, and ask for a hearing test avd a referral to SaLT. They will want her to have had a hearing test to rule out conditions like Glue Ear.
I would also ask the School’s SENCO to assess her and speak to your School Nurse Service for advice.
We’ve found that reward charts and punishments dont work either. Have you ever been recommended the books The Whole Brained Child or The Ecplosove Child? If it does turn out that she is ND then the traditional methods of child discipline you’ve been trying are unlikely ever to work.
If you think she has ADHD I would also try interacting with her as though she has. How To ADHD is a good resource avd she’s quite engaging.
Doing things like giving her a regulating activity like TV in a room away from her siblings with a drink and a snack after school.
Upping her protein but not from UPF sources.
Introducing Meditation. There will be plenty of guided meditations aimed at DC on YouTube.
Also upping her exercise. So something like an athletics or cycling club, cricket or martial arts or even just starting the C25K with her. There might even be a Tween Yoga class near to you?
Do have a think too about applying for an ECHP. They are based in need rather than diagnosis avd the MNers who hang around in the SN Children Section should be able to help you with this.
If I could go back in time i would have pushed much more at this age so that my DD would have had an ECHP and diagnosis to help her through High School.