I'm not sure what HHI means. I can tell you, though, that dealing with DD's situation has been my full time job. It's a luxury and I don't know how it would have worked if I wasn't able to be a full time parent. Or if I had other kids to worry about. There are folks here who juggle their 2E situations and have careers - professors, psychologists, lawyers - all are on the board. And some of them have multiple 2E kids. I can tell you that there are peaks and valleys. You WILL have times when things go smoothly. When you can breathe. When you can concentrate on work or a hobby or maybe even reading a novel just for fun. But you will also experience times when your child is having an issue, school seems to be falling apart and you have a nonnegotiable deadline at work. All at the same time. That's the reality. But you have found a good resource here. You are among parents who get it and will be there to a lend an ear and a supportive shoulder to cry on. Use us.

As to your questions - first take a deep breath. There will always be "what ifs" and "how abouts". Our kids are outside the box - it's counterproductive to try to force them into a one size fits all solution. It won't work.

I can tell you that I insisted on a no homework policy for DD. She has SO many LD issues just processing all the information that comes at her throughout the day can be overwhelming. She is extremely focused and hard working so I argued that asking her to do more after school would be too much. She would get overwhelmed and be unable to focus as well at school and that was our priority. It has worked well. No math worksheets, no spelling tests. She does project based assignments but no busy work that would overtax her coping strategies. (At one point she got a disgnosis of NLD. I got this argument from my research into that and still use it even though NLD is no longer considered a valid diagnosis for her. The principal remains the same.)

With a 2E kid you HAVE TO GO THROUGH THE STRENGTHS to address the weaknesses. Make this your mantra if school doesn't get it.

Forget concerns about coddling. Is he choosing to behave this way or is there some neurological issue underlying it? "Coddling" would mean rewarding a choice to behave badly. From what you have described I'm not sure he is capable of making that choice. He has to first learn a coping strategy and a way to behave appropriately before he can be accused of choosing to behave the wrong way.

He may need a 1-1 para in school. Another reason to get rid of "homework". Call it "school work" and have him do it under their supervision. At home enrich, enrich, enrich.

It sounds to me like he is highly anxious and functioning in fight or flight mode. He panics about not being able to control his responses. I think he needs a supportive nurturing environment rather than a punitive one that will treat these reactions as chosen behaviors. JMHO...

And you can use that love of researching and building. "When the math worksheet is finished I have an idea for an awesome project" would be better than "if you finish the worksheet you can do your project". One makes it a given that he has to get through the dreaded task and the other comes across as something he can get into a power struggle over.

From what you've written so far I don't see homeschooling as a viable option. At least not yet. You need some more tools first. I think you and he would both burn out if you tried it before he was ready.