I can't help you with the insurance stuff or referral, it is too alien to what we have.
But one thing I could suggest - can you talk to this "I don't know" caseworker and try to get a decision of sorts out of her? The pediatrician our kids see is sometimes like this - he's a nice bloke and a good doctor, but he really hates to commit to anything. A lot of time when official letters are required, you almost have to dictate it to him. He won't say anything he doesn't believe in, but he does need to know what to say.
Maybe Nate's caseworker is a bit like this? In which case, if you say to her, "Nate is a great kid but he really does have problems. The fact that you've been assigned to him makes that fact obvious. He really would benefit from help in a number of areas including school, but we must have a clear and hopefully correct diagnosis for the most appropriate help. We also would like to know, as his parents, what is the best way to help this child and not hold him back. We must know the right way to proceed. Please help us get this assessment. I've already made some enquiries, we've been told that the most appropriate person to assess Nate is a neuropsychologist. I need your help to make tis happen. While I can make enquiries and talk to other parents via support networks, I need you to dovetail your services from there."
If she quibbles and tries to say, "We can't go straight to neuropsychologist; there are procedures we have to follow, etc etc" then say to her, "These are things that YOU know. Fair enough. But what I know is, he could get sent to one specialist, then another, then another, and time passes and we still probably won't get a sure answer. Eventually someone will refer him to a neuropsychologist, but at this rate he will be in his 20s. Let's make it happen now, and save not only time but money in the process."
If she keeps saying, "I don't know," then tell her, "We must find someone who DOES know, then." Alternatively you can say, "You mightn't know, but I do - this is what we need. Now I need you to make it happen. I will help. Here is the doctor's name I want. Here is the form; this is what you need to write. Thank you for your help."
As for why he did so well at Hershey Park - I suspect it was the interesting, stimulating environment. Some kids seem to desperately need a stimulating, enriched environment. For them, life needs to be one long, intense, university-level education course.
I remember reading years ago (I was barely out of my teens) about research into Downs Syndrome claiming that the best way to give a Downs baby a good start in life, to give them the best chance to do as well as they could, was to get rid of all the usual baby pastels and pretty flowers in the nursery, and replace it with strong primary colours, alphabet blocks, puzzle toys which are multi-purpose - all the stuff you can find which is designed to stimulate the baby's mind. difficult child 3 has a drama classmate with Downs, I asked her mother if these ideas are still in use. Apparently they are (or at least still were, when their daughter was a baby).
If you can do the same sort of thing for your son, only at a three-year-old level, it might reduce some of the problems. For example, if you have some fun but educational books for him, or computer software for him that is educational as well as fun - it might reduce his boredom AND keep his mind stimulated. Begin with age-appropriate stuff but if he shows aptitude or interest in a particular area, follow it along and let difficult child choose the level he can handle.
For example - when difficult child 3 was a baby, I didn't know I had aGFG. I thought I had a bright easy child who was just a bit slow to talk. I used to sing to him as an infant, we would walk and I would talk to him about what we saw. When I sat at the piano to play, difficult child 3 was on my lap. When difficult child 3 reached out to touch the piano I could hear that he was musical - he never bashed at the piano the way babies do, but instead he would softly press the keys, one with each hand. I noticed fairly quickly that he was choosing note intervals which were harmonics and not discords. He quickly showed a preference for some tunes I played over others and tried to copy them. By the time he was able to sit at the piano himself, he was trying to reproduce tunes he liked best, of the ones I sang to him. By about a year old it was clear that his favourite was Twinkle Twinkle - it's also the alphabet song. He was saying the names of some letters, so I used a simple computer program to let him learn the alphabet. I then labelled the piano keys with the note letters and wrote the note letters for Twinkle Twinkle on a sheet of paper. He then used this sequence to remember how to play it.
It was a short step from there, to writing the note letters on manuscript with the notes on the staves. By 18 months difficult child 3 was reading sheet music.
All I did was follow difficult child 3's lead. He eventually reached a certain point in his music education where he couldn't go any further. His interests diversified and he no longer plays piano much, although he can. He's now much more interested in a number of his school subjects especially electronics and information technology. So we bought him an electronics kit. He has access to computer games plus we Do provide an enriched environment - when we go to the beach and I see difficult child 3 carefully pouring water from a bucket onto the sand, I ask him what he is doing. If he is studying the way the water and the sand interact, I sit with him and work with him, talking to him about erosion. We make observations together. In this way he has learned the concept of scientific hypothesis and how to test it. All we did was give a name to what he was already doing.
On our TV are educational TV shows for senior high school science students. difficult child 3 watches these and is learning about organic chemistry.
Providing opportunities to learn and to explore interesting things are often really important for our kids. But often a difficult child doesn't know where to start, or HOW to start. It's a matter of watching them, and trying to give them more of what they seem attracted to. It also involves spending more time with them than a lot of parents would.
I don't know if this would work for your difficult child, but I'm wondering if it would help. it might be interesting to try it and see what happens. Whether it succeeds or not, you could get some interesting information out of it.
Marg