It turns out I was worrying too much about whether or not Alex's school would reconsider integration. They don't think he's quite ready for that but say he's making good progress and things are still on track.
He's doing very well in school, working independently for rewards. He's listening and even showing signs of self-regulation.
All of which is better than he's doing at home.
I can understand it. I've seen any number of studies showing that willpower is a finite resource. People put through a stressful test of self-restraint tend to overindulge in food or other pleasures afterwards.
Listening is work for Alex. It clearly takes up a great deal of effort. When he compares the rewards at school, therapy and home, he's choosing to put his effort into school and therapy. (Which both also happen to be shorter duration with more frequent reward points.) Home is safe, where he can relax. Unfortunately, that makes it more unpleasant and difficult for us.
I'm trying to be patient and understanding but still set down consistent rules and consequences. Hopefully, things will improve.
His music teacher suggested we consider Sensory Integration Therapy. We did that before when he was little but he began objecting to it, so we let it phase out. Maybe it's time for some more deep pressure techniques.