The frustrating thing about evals for spectrum in homeschooling is that there aren't necessarily enough people seeing the behaviors to make it easy to get him diagnosed. The system is set up for people in school and wants you give forms to multiple people. We did that, but nobody was ever seeing him in longer than 20-30 minute snippets and usually in preferred settings, like a swim class. Makes it really easy to get unhelpful results.
You should do the evals, but I'm just giving you the heads-up about that issue. If you don't have people with him enough to see what you're seeing, they can't mark it on the forms. And yes, what you're seeing sounds like important stuff. Some of that sounds like perseverating (being stuck on things) and repetitive behaviors.
Why can't you play characters while you do school? I mean, I'm all for getting instructional control, blah blah, but every professional who has come into my home and tried to work with my ds MET HIM WHERE HE WAS. You're going to get a lot farther meeting him where he is than rigidly telling him this is what school looks like.
You can look for Play Project by Solomon to see what it looks like. I've been reading the book, and it's a lot like what our behaviorist has done with us. If you could find a Play Project trained therapist, they might be useful to you. It's just a really good lead-in to homeschooling, because homeschooling is so driven by relationship, communication, integrity.
I have no doubt he's both challenging and charming.
You try starting a thread that says suspected aspergers and K5 and see what you get. Or keep reading the boards and using site search. My ds has SLDs on top of his autism, and honestly his support level may be a bit higher than your ds'. With my ds, I could do really out there stuff (looser, less predictable) like Barton, but it made it really hard to get instructional control. We switched over to very predictable, incremental materials. They fit his SLDs and lower his anxiety. I'm not saying you should do that, only that I did. Initially it was to make our ABA go better, because my workers couldn't work on behavior AND do really out there kind of teaching. And I can teach him now, but honestly it's just astonishing how CALM he gets with running through a pile of really predictable work.
Again, I'm not saying turn all your world into that, but you might just see. And if what you're doing fits him, fine and dandy. Just saying it works well for my ds. I use a lot of printable workbooks I get from Teacher Created Resources, Evan Moor, Carson Dellosa, etc. I was just downloading more tonight. So anything I might have been wanting to do with a more typical school subject or homeschool curriculum, I look for from these publishers. I'm able to hand him one page at a time, keeping a consistent predictable structure, and it just lets him get in a groove.
One of the things my workers wanted was a balance of independent work, seat work, and together work. Does he have behaviors with waiting? Can he busy himself in a non-preferred setting? My ds couldn't, so working on independent work is actually a huge goal, because it's helping him go oh, I could sit down with something and make a choice and busy myself. Not the falling into the aut, getting lost in a pile of things by lining them up for an hour kind of gig, but actually just choosing to work on something either handed to me or from a list of choices. That was really hard for him. For that I use super simple things like word searches, dot to dots, mazes. Anything at his level that he has done enough with you that he can do them independently could be put on his list. For K5 age, you're talking a super short time, super short. It could even be something like look at picture books or play apps on the computer or whatever. It's just another category.
Yes, it's super hard to tease apart the ADHD piece and the Autism piece, sigh. My ds *looked* astonishingly ADHD but he passes attention tap tap computer tests with flying colors. He failed one before he got his reflexes integrated, but now he passes them. So my own two cents of advice would be to see how far you can get with OT and getting any retained reflexes integrated, bring in a behaviorist to help with the behavior, and then if his behavior *still* impedes his ability to access his education or he is a danger to himself or others, then pursue the meds.
My ds needs a LOT of movement in his world. We just got back his genetics testing, and ironically it turns out he has fast twitch muscle fibers and another gene associated with muscle strength. Like literally when his coach was telling us to get him in running, that he's a sprinter, it was for real.
Is your ds doing well on the list of things in your sig? Is he getting through it? He seems very advanced. The advice I've been given a lot is to focus on behavior with my ds, because the academics are, in a way, the easy part. It's something to consider. Like not in a hard slam, crack down kind of way, but more of an equal effort, bring the social and the behavioral pieces online. When we got our diagnoses and got the behaviorist in, we were able to bring in Social Thinking materials. If you bring those in, you're going to use up some of that brain power. He might be putting tons of energy into math and you're like this is awesome, this is a super power! But in a way, it's really imbalanced. If you divert some of that energy to Social Thinking, to learning about self-regulation and Zones of Regulation and 5 Point Scale and whatnot, it might literally slow down his academics. It has for my ds. Any are where we do a lot of therapy diverts brain energy and slows down progress in other areas. But it might be kind of welcome in the end and might balance him out a bit and make him easier to live with.
And you know, if he's driving it himself, way awesome, so awesome, go for it. But it's just something to watch for, that it might slow down or balance as you step in some interventions. Sometimes I feel bad about that with my ds, but I don't. He's more balanced that way.
Fwiw, given how high he's performing right now academically, I wouldn't go to a small town, local psych. You might get more helpful evals if you go to a psych who specializes in gifted who has a lot of experience with autism. You'll get a more thorough analysis and better advice on how to proceed. You might get validation of out of the box things you're doing, rather than pat or inexperienced answers. Evals are a big deal and worth driving for.