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You have some variables that definitely complicate things, and I've been trying to think if I have anything useful to contribute on those. And ... am still thinking.
Normally, probably 90% of the time, I think diagnosis and having a "label" is a positive thing for ASD kids because, among other things, it gives them a logical explanation for things they are observing on their own. Without it, they fill in the gaps their own way, and the logic can be very off-base. I worry that things like your son's mental inventions stem from this; he is observing the world, trying to sort out how he fits in, and is reaching false conclusions. But, the flip side is that in his case I'm also nervous about how he might misuse knowledge of ASD. In the end, it very much is a "know your child" decision.
When it comes to figuring out how to help him, overall, I guess I want to know what he WANTS. Not what he thinks he should want, not what he pretends to want in order to fit in, but what he really, really wants. Many solutions involve appealing to what the child wants, while teaching them what it is they actually need.
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Mom to an amazing young adult AS son, plus an also amazing non-AS daughter. Most likely part of the "Broader Autism Phenotype" (some traits).
Schools in the US are required by law to provide support for "functional skills" even if a child's grades are not impacted. This means if your child has a deficit in social skills or pragmatic (social) speech or executive functioning (organizational skills) they are supposed to provide support for that, even if he doesn't need academic supports.
Lots of schools don't want to spend the money on supports for kids who are doing well academically - our own school told us they could not provide supports for my son even though he was violent at home and suicidal, since it wasn't (usually) happening at school. Later, we used our health insurance to get a full assessment, and they told us the school was wrong - there were supports he should have been getting.
Your first step, should you choose to go that route, is to request that the school do a formal assessment of your child. You need to do this in writing. Make sure that you indicate specifically that you are concerned about social skills, social speech and executive functioning. He should be seen, at minimum, by the school social worker, the school psychologist and the speech therapist (you may also want the Occupational therapist to do an assessment as well.)
http://www.wrightslaw.com/blog/?p=694
http://www.wrightslaw.com/blog/?p=4033
The next question you asked is whether or not you want the label. I can only answer for us, but since my son is high-functioning enough to be able to "cover up" his disability, the label is really helpful to us: it provides a frame for behaviors that otherwise appear deliberately rude. We use it with other adults in charge of him only (e.g. teachers, etc.) and leave it up to him whether or not he wants to disclose it to his peers.
The label put my son in the category of "disabled" and thus eligible for supports like an IEP that they refused us without the label. I would agree that a label is only as good as what you get out of it: for us, it means he gets a certain number of hours of certain therapies every week at school, and also that teachers and administrators keep an eye out for him during lunch and other "free" times. Totally worth it for us.