We went through a process much like aeh and spaghetti describe with DS10, then 9, last year. He was miserable at school, having anxiety/panic attacks, resisting attending (he had a lot of mental health days at my office), having his areas of strength ignored and his second E mismanaged - it was comprehensively bad and had been going downhill for some time. I had been looking at other options and found a school much like the one you describe. DS was adamant that he would not change schools, believing all schools were awful and he might as well stick with the one he knew. Rather than start with telling him about the school I thought would work, I had a number of conversations about different learning environments, styles of teaching, educational philosophies and used the example of his preschool versus DD's preschool, how both of those differed from their current school, which differed from a friend's school. I moved from there to discussing the many different schools I had looked at and what was similar/different amongst them, and how they compared to current school. Then a discussion of pros/cons of current school and how school x compared. After all those conversations I suggested that the best way for him to figure out whether he liked school x was to take it for a test drive.
I went to great lengths to make sure he knew that the question was whether the school was a good fit for him. Not us, not the school, him. I assured him we would not even consider sending him there if he didn't think it was a fit (and said that we wouldn't be considering he visit for a day if we hadn't already satisfied ourselves that it might be a fit). I also told him that we had learned a lot from our experience at the current school and would never again try for so long to make a school work for him. We would pull him out if things went sideways. He was so distressed by the idea of changing schools and so beaten down by school that he needed to know even before visiting that it was his call, that we had extensively pre-vetted, and that he wouldn't be locked in to the decision. Oh, and I dropped lots of random nuggets, as aeh suggests.
That took weeks (!), but it led to him spending a day at the school, paired up with the head of school and a teacher throughout. Afterward we talked about all the sorts of questions spaghetti sets out - classes, teaching, kids - and how the day compared to an average day at his current school. I particularly asked how both his favourite and least-favourite subjects compared. He was fairly positive, but told me he needed to spend another day there to be sure (I only suggested one at first, because I knew he needed to see this as a minimal commitment).
We did a second day about a month later, and there was some renewed opposition to the idea of changing schools, beforehand. I reminded him of his own comments after the first day, nothing about my thoughts, just his own, and that helped him regroup. The second day was wonderful. He made a friend, was excited about what they had learned, expressed disappointment that something he'd really liked the first day wasn't on that day's schedule, talked about some policies he really liked and how they were different from his current school. The next morning, en route to the current school, he said he'd made up his mind and he was going to school x the next year!
Getting his buy-in, to the extent that he felt he was the one making the decision, made the change manageable for him and told us we were making the right choice (he was moving with or without buy-in, but he was 9, not entering high school as with your DS).
We had to get through another 5 months at the old school, which wasn't fun, but we're now almost 10 months in at school x and it has been largely a success. DS is happy & doing well. When he has a reflexive 'I don't want to go to school' moment (rare, now), it just takes a question about how the previous school day went to redirect him.
Good luck. The school change has been transformative for our family and I wish the same for yours.
