Regardless of the debt, I can't help feeling the school DID let him down because there was one unyielding strategy to deal with him and it simply wasn't working. I am not going to aggressively pursue this but I could tell they had just given up on him. I was in a panic and did not want him to have an expulsion on his record. In the final meeting, the head told me he felt my DS was in the "wrong school", it didn't feel like much of an olive branch or offer much hope. He told me he had serious concerns about where DS would end up.
The thing is that you can feel they let him down all you like, based on what you've shared it wouldn't give grounds to argue they've failed in their side of the contract.
For example
If schol only had one strategy and it really wasn't working then I would have expected a parent to be on the phone and arranging meetings long before KS4. Schools will follow their behaviour policies.
You then say that he got minimal pastoral support because his tutor didn't 'get him' one year. Was this discussed with the head of year? Or was it ignored and pulled up later as a way to justify why his behaviour wasn't his fault? If the lack of pastoral care was such that it directly caused your son's behaviour then did you request a tutor group move?
If my child was genuinely only ever in trouble for some time keeping and disorganization then I'd have been on the phone to heads of year and senior leadership the moment it became a trend. The fact you didn't and accepted years of higher level sanctions for apparently only minor issues means you've either ignored it but subsequently want to blame them for your son's situation, or there was much more to it as schools tend not to get to exclusion talks over a little bit of disorganization.
If your child's academic performance was such that you had concerns about SEN then that would have been an issue to raise long before the point when the school said he is facing exclusion.
A head saying that this isn't the school for your DC is something many heads say when a student is getting to the point of being permanently excluded, especially if the situation had gone on for years. Heads draw the line somewhere and they made their position clear that if his behaviour didn't improve the exclusion was on the cards.
If he's got poor GCSEs then that's not ideal, but it does tend to come with the territory of spending 4/5 years of secondary education behaving in a way that leads to repeated detentions/isolations/heading for exclusions.
I see students mess on and get excluded (fixed term usually and occasionally permanently) and one of the common trends is for parents and students to try and find every reason under the sun why it's never their doing and there's usually years of minimising the behaviour. I can think of occasions where the system (in these cases state) have failed students with moderate to complex SEN, but their parents were proactive all the way, never made excuses, and they were heartbreaking cases. This doesn't sound like one of those.
I'm glad you aren't planning on taking a complaint because it would be unlikely to be fruitful, but they're the reasons I think posters who are advising you to launch action against the school and argue you don't have to pay are hugely misguided.