Sorry to come to this so late, and I really hope you've had some clarity in the meantime. Can I absolutely BEG you to track down some books on giftedness, specifically with regard to intensities? I'm reading "Living with Intensity" eds Susan Daniels and Michael Piechowski atm; "Emotional Intensity in Gifted Children" by christine Fonseca is also a good intro to the topic.
BIG alarm bells started going off when you started talking about the school wanting a psych profile - especially if they are talking about Aspergers/ASD - and you touch on this a bit but it needs to be said: a lot of the characteristics of SOME gifted children - particularly those with intensities - DO crossover with those of ASD children. The intensities themselves are NOT diagnostic of ASD, but they can be misread as such.
There are basic differences between a child with ASD and a child of high intelligence and severe intensities that a good developmental pyschologist with experience in giftedness AND ASD should be able to pick out.
My daughter is low level gifted with high level intensities; it was suggested at one point that she had ODD (different diagnosis, same problem) because intensities are so badly understood by the educational system. A brilliant teacher not experienced with gifted children will ALMOST ALWAYS be concerned about what turns out to be pretty typical - and relatively easily managed - behaviour.
My daughter is in the best possible environment for her academically, but there are still social concerns that crop up because she is just so much MORE than other kids. More sensitive, more thoughtful, more angry, more rebellious, more critical, more outspoken (do I need to go on?) She will not, for example, allow anyone to stop her midthought or midprocess (painting, sums, writing, whatever) and finds it very, very hard to shift focus from one thing to another. Her teacher has learnt to accomodate this by giving her a much longer lead time than the other kids require ... "don't forget you have your clarinet lesson at 2pm, A. Maybe just make notes for now and start your story later ..."
She also often seems very far away when she's working, and can be hostile if interrupted ... we are working on responding nicely if people have questions etc, but there's also been group work done on "thinking face" and when it is and isn't appropriate to bother someone.
And concentration for her isn't the same as for other kids - she can be talking to another child, sketching something AND listening to the teacher reading, all quite capably. What most teachers will peg as "doesn't concentrate/listen" can actually be "doesn't look like she's concentrating or listening but can actually recite book/instructions/whatever word for word".
Then there's the basic stuff like wanting to spend a lot of time alone one day, then needing lots of social contact the next. Swinging between aloof and friendly, which is confusing for other kids. Well - there's a world in her head, and sometimes she wants to spend time there alone, and sometimes what other kids are doing seems interesting and fun. And when it's interesting, she wants to beinvolved with 150% of her being ...
This is often misread as social immaturity, but it's not. It's just her, and given the tools to help control and channel her intensities (and accept that not everyone feels the same way about things, and that no everyone CAN understand), she does much better in the classroom environment. Small behavioural tweaks can yield major breakthroughs, because what comes easy to the 95% needs to be worked on by the 5% and vice versa. (You'd think that concept was easy to understand given the vice versa, but it's actually a hard lesson for most teachers - just a child learns easily, doesn't mean they have automatic control over all their senses or emotional responses.)
As to testing - I would pursue it if at all possible. You should be able to get basics on Medicare, I think - a rec by the GP to a behavioural psych? Excluding the possibility of ASD is probably the most valuable outcome - you can then talk to his teachers and explain that your son has some behavioural quirks BECAUSE of his high intelligence and they need to learn work with him, rather than against them.
Funnily enough, most of the suggestions for working with high intensity kids are equally applicable to working with ALL kids, and should probably be standards in the classroom anyway. But when it comes to the 5%, a little bit of understanding that some kids are MORE makes everyone's life much easier (including the teacher!)