Back again. My DD had a very late diagnosis of Aspergers early into the A2 year, which was too late for a statement. She was going into school and walking straight out again due to anxieties with noise levels and people, which we didn't realise for a while (moved from a small school into a big comprehensive for her sixth form years).
We enlisted the support of the Head of Year, the school counsellor and eventually the social services team via Connexions.
She was allowed to access practical assessments at school, dip into what lessons she felt she could cope with and enter the exams as an external candidate at the school (school also arranged for a separate room/invigilator where she could sit the exams in isolation).
I would urge you to speak to and keep the current school involved as much as possible and keep them on the hook (duty to provide access to education).
I've heard good things of Nisai, but we went and found a private tutor to support DD. Her teachers really wanted to help outside of school, but didn't have the capacity or time.
My DD will persevere with most things, and did have an end goal of further education after school (waiting for her exam results at the moment) - PP is right that your son needs to be motivated.
Separately, DD is having counselling for anxiety related to her diagnosis, which is helping a lot.
Best wishes for you and your son. If you have questions, I will try and help further.