Therapy and support for teenaged son

I'm looking for advice about how to navigate NHS services and (more plausibly) what would be most appropriate for private therapy for our son.

My son is 16, has an ASD1 and tourette's diagnosis;  he's currently not able to go to school as he's had a very serious and distressing time with his mental health.  He is, in theory, under the care of our local Camhs, but more than 7 weeks after he made an attempt on his life, they have yet to clarify what a treatment plan will look like for him.  After multiple calls, emails, some pressure from our GP and speaking to countless other services, we have finally had a meeting with the Camhs psychiatrist. But we are being pushed back by the promise of a CETR review, which was put into play because I took my son to A&E when he became very distressed and this was what the Camhs liaison person deemed appropriate at the time. We were promised a CETR panel meeting within a week and 6 weeks later have no date, there is no contact number of working email, and every time I call the Camhs liaison at the hospital, they say they can't help. It feels like the CETR is another layer of bueaucracy that's creating further delays and confusion, when we urgently need help and someone to advocate for him (aside from us, we're obviously focussed on this but have reached a complete bottleneck).

I know we won't be the only people in this boat with Camhs, and are probably further along the road with some, at least we're not on a waiting list as he have been in the past. Does anyone have any advice about dealing with Camhs and how to best navigate the system and escalate this, without feeling like we're shouting into a void, would be much appreciated. There doesn't seem to be any normal accountability or line management, so the 'who's in charge' question gets left completely unanswered, as are questions about decision making and timescales. We're trying to stay in the system so that we can be referred on, if needs be, but it's incredibly stressful and worrying.

If we were to go private, does anyone have advice about what the best kind of therapy is, recommendations or can signpost me?  The therapy our son had from Camhs in the past but it wasn't great - it was very mainstream, reliant on our son being articulate about his feelings (not easy for an autistic teenager) and not remotely adapted to his differences.  Our son is very bright, masks to a very high degree, can be demand avoidant and has struggled with a late autism diagnosis. He's completely lost his confidence, has really struggled at secondary school  which has affected his attainment and self esteem very badly and despite being outwardly social, with a consistent group of friends, has now completely withdrawn from friends.  He is extremely unlikely to be sitting his GCSEs this year and given what's happened, we've reduced demands almost completely.  He's got an online lesson for an hour or two a day with his TLA and the school are trying to see if the exams boards will give him special consideration, which would be a huge help. He's getting as much rest as possible and he's calmer at home, with school out of the equation, but without some treatment we feel that he's unlikely to recover and regain some confidence.