Boy, I believe you when you said, "I have Googled and read and read and Googled until I just couldn't read anymore." The length of your original post shows how much you care. Hopefully, I can help. And I'm pretty sure I have a few sources on tap that you haven't found yet. I've got a lot to say and I doubt that I will get it in all tonight. And then I will be out of town for two days. I want to talk about the ADHD diagnosis. His age and place in school. And maybe most importantly ways to work with him that will be more productive then what is going on now.
You ask if he has ADHD. The answer is probably, but there are a few questions/concerns I have.
The first concern I have is from a very large study in Canada (more then 900,000 children) that found, " The youngest children in a classroom may be more likely to receive a diagnosis of attention-deficit/hyperactivity disorder (ADHD) than their older peers." The lead author stated, "It could be that a lack of maturity in the youngest kids in the class is being misinterpreted as symptoms of a behavioral disorder," from - http://www.medscape.com/viewarticle/759900?src=nl_topic
Now this doesn't mean that he doesn't have ADHD, but it is something to think about. Your doctor did the correct thing in doing the survey for both school and home. Perhaps the only place that did not follow the guidelines was the immediate prescription of medication.
The New Clinical Practice Guidelines say,
Special Circumstances :Preschool - Aged Children
Clinicians should initiate ADHD treatment of preschool-aged children
(4–5 years of age) with behavior therapy and should also assess for
other developmental problems, especially with language. If children do
not experience adequate symptom and functional improvement with be-
havior therapy (most programs are 10–14 weeks long, but the clinician
should check with the therapists about their usual length of intervention), the clinician should first evaluate the adequacy and parental acceptance of the therapy. If the symptoms and/or functioning have not improved and the child is at significant behavioral or developmental risk because of ADHD, medication can be prescribed." -- American Academy of Pediatrics. Implementing the Key Action Statements: an Algorithm and Explanation for Process of Care for the Evaluation, Diagnosis, Treatment, and Monitoring of ADHD in Children and Adolescents -- http://pediatrics.aappublications.org/content/suppl/2011/10/11/peds.2011-2654.DC1/zpe611117822p.pdf
I think my main question would be - is your doctor a pediatrician? The reason I ask is that, your son might well do better with a psychiatrist or a psychologist that has more experience with ADHD kids. However, some pediatricians have lots of experience - so it all depends.
I guess the main reason I bring this up is that even though all the symptoms do point to ADHD, there are some things like Sensory Processing Disorder that have very similar symptoms and I would want somebody with experience to possibly rule other factors out.
One of the things that I do find unusual is the length of time he crys. As an elementary school principal, we had kids that did cry in kindergarten. They usually stopped after a period of time. His crying is unusual. And that made me wonder about SPD. Many of the things that you mentioned are symptoms of SPD, so its probably worth checking out. And SPD is treated very differently in some respects to ADHD (no meds) This is a good site to look at -- http://www.sensory-processing-disorder.com/sensory-processing-disorder-checklist.html for symptoms and we have our own specialist on medhelp if you have any questions here. http://www.medhelp.org/forums/Sensory-Integration-Disorder-SID/show/1396
So do take the time to check out the SPD site and our own site (just read through some of the posts).
A few questions now. (besides what kind of a doc are you seeing?)
You said, "He doesn't run away anymore, and he hasn't kicked walls. He just cries when they do math, or an activity he has trouble with. He does get in trouble for being too wild sometimes, like taking his jacket and swinging it around causing it to hit other kids."
So he is not crying as much in school? Overall, would you say he is doing better with the shortened day? Is the staff seeing an improvement?
Does his teacher notice any of his apraxia? Is he eager to be called on. Is his hand up to volunteer answers or does she have to coax him to talk?
So, in conclusion, this is a pretty long post to say I'm not sure if it is ADHD or not. Hopefully, you can see why I do have a few questions. Now if it is ADHD, there is a lot that you and the school should be doing differently. And that is gonna be a whole much longer post (probably). And I do have several suggestions on how to change his behavior. It kind of appears that your way has not been real successful. And if he does have ADHD or SPD, I can guarantee that what you (and to some extent) the school) have been doing will not work.
But something to do over the holidays. The little guy is obviously frustrated. Kids need to be taught how to handle anger and frustrations.
Look into buying "Cool down and work through anger" or "When I feel angry". This is part of a series of books aimed at 4 to 7 year olds and meant to be read to them at night (several times) and then practiced. Kids do need to be taught how to deal with anger. You do not try and use these techniques while he is crying. But once he stops or later on in the day - you can refer back to them or pull the books back out. And at the bottom of the page you will find other books that may also help.
You can find them here - http://www.amazon.com/Cool-Through-Anger-Learning-Along/dp/1575423464/ref=pd_sim_b_5
I hope this has not been too overwhelming. Get back to me if you wish with the questions I asked - (oh quick thought - anybody in your families have ADHD?). Best wishes. Once I hear a bit more from you I will suggest a few ways to help him change his behavior (though the books I mentioned will help a bit I think). Best wishes.