I had to search for the acronym, not heard of it before but understand the term now.
www.autismeye.com/fabricated/
It's almost impossible to give any advice without knowing age and sex of child and the problems you see but school don't.
All I can say is, if your child has a condition, or more likely several, then you need a firm diagnosis. Unfortunately that often means years on waiting lists to get an NHS accredited diagnosis.
It may be that your child has an unusual presentation of symptoms. It may be that the professionals you've seen don't have all the information if you have private diagnoses as well as NHS ones.
If it's learning support you're wanting to put into place, then tests like DISCO, ADOS etc. should show any needs. Ed Psych, SLT, sensory OT and Paed, particularly when working in a team would be a good place to start.
Can you find a professional who works part time for the NHS then see them privately to save a long wait?
It could be that your child is only just meeting all the targets for school and they don't see the need for any interventions. It's absolutely amazing what some schools "don't see"
I'll stop speculating, all I can really do is repeat that if you want school to put interventions into place then you need a firm diagnosis with a report which states what interventions are needed at school and at home.
You may also find that a different school would see your child's needs and act on them. It happens.