I was in a similar situation. I suspected DS had AS and asked for 'an assessment' from CAMHS (didn't know about ADOS, MDT back then). A single psychiatrist observed him in a 1:1 situation and noted that he made eye contact, engaged with her, but didn't take any information from me or from school. On that basis she said that he had attachment issues due to his early life (was looked after by grandparents and raised by me as single parent).
I didn't agree and went to a private paed who made a clear dx. Had to borrow to fund it but I think it was the right thing to do - you can push for a second opinion but I didn't know how long that might take. DS was older than your son so I feel that time was against us. I'd say your situation may not be so urgent, but then again earlier intervention is always better.
I subsequently got other assessments done as part of DS' statement and there were NO professionals who disagreed with the private dx (and many who were baffled by the first dx).
I had a meeting recently where the CAMHS psychologist admitted that there were clear AS traits all along and there was absolute consensus that the AS dx was correct.
I would recommend looking at BIBIC - they do assessments which look at needs, but not diagnosis. £50 for two days (plus travel/accomm). They provide a therapy programme to carry out at home as well - frankly probably more helpful than OT you'd get on NHS (but I wouldn't know, we've never had any).
If you do pursue a private dx, choose your paed/psych very carefully - mine was also an NHS paed and very well respected.
I was never offered a parenting course, but was given therapy, which I went along with. I don't feel it was necessarily suitable, but it wasn't damaging and it meant that we were still getting access to services and showed willingness to be a supportive parent. So I personally would go along with the parenting course, if only to be able to say 'we've done this and the problems still remain'.
I would also say that the most useful interventions are often provided by the parent in any case - things I've learnt from books or workshops. You don't necessarily need a dx to access these. So if you feel that some of the strategies will help, give them a try and don't worry about whether the label fits. In practice, I think SALT/OT which is provided isn't much more than giving exercises for parents to carry out anyway.