Behavioural issues are barriers to learning. Im assuming your dd doesn't have a diagnosis?
In the meantime you could ask your GP for a referral to a paed and a sensory trained OT (long waiting list). You can also ask for a referral to SALT, if your dd has any speech, language, communication difficulties. Not necessarily an obvious speech delay etc, but difficulties with social interaction or communication for example or attention and listening difficulties.
You could ask the school for ASD Outreach worker, who are far more readily available to schools (you don't need a dx of ASD, just ASD 'traits')
With all due respect to SENCO she isn't an expert!
School might well respond badly to you applying for SA, as some see this as a criticism, which is more a reflection of them, not you. Make your concerns clear, in line with what the Law defines as progress SEN COP (in my experience some schools are not even aware of this and again don't take kindly to their inexperience being pointed out). However, they should be able to be professionals about it.
It is not a criticism of the school, you can see that they are trying very hard to help you dd. However, as a parent and your dd's advocate, you would like to exercise your right to apply for SA (with their support if poss) to identify and fully understand your dd's difficulties and how this could be interfering with her learning as you both in agreement that she is struggling in the junior environment.
Why would any school object or take offence to having a struggling child's difficulties identified!