My dd Is globally delayed with possible autism and learning difficulties, it took us a long time to get the help we needed cause we were just being fobbed off. I would say information is key, get as much as you can from both schools like you said and maybe write a diary of his behaviour. If my dd gets sensory overload she puts a blanket over her, I think it's her way of having a few peaceful minutes and just blocking out the world. Sometimes if she's told no she will lash out and hit very gently. She isn't fussed about routine but I have read that if a child likes routine and they are taken out of it it can cause major problems.
Like someone else said, don't get fobbed off and keep pushing till you get the answers you need
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