Thanks. I do not doubt that you want the best for your son. I spoke my piece because I have had a lot of experience homeschooling children, including tutoring other peoples' kids, many of whom were not good learners and/or did not have the right kind of atmosphere at home in which to learn.
As an example, last year I took care of and taught for 4 months an 11 year old girl who couldn't do her grade level. Her handwriting was terrible, she would spend 4 hours on a page of math that should have taken 20 minutes. She would whine, gyrate, and do anything and everything to not do her work. Her attentions span was miniscule.
This is what I did:
1. Made handwriting a priority. Invented games and wrote interesting sentences for her to copy. Had her do lines of letters, gradually doing the whole alphabet and then letters mixed. Concentrated on this until a few weeks later her handwriting was beautiful. Made her sharpen her own pencils and made sure she had plenty of pencils.
2. Started a "20/5" schedule. I only allowed her to do schoolwork for 20 minutes, then she had 5 minutes to do whatever she wanted - read, run outside and play, whatever.
After a few weeks she was begging me to extend the 20 minutes. We extended to 25 minutes, and then she had to do something physical.
3. She got to engage in her favorites activities on a regular basis, we would intersperse them with the stuff she didn't like. She was very artistic, and loved crafts, so we would do (for isntance) math/beadwork/handwriting/drawing/finish math/ etc. Of course, in between each 20 minute segment she would have 5 minutes off.
4. I had her do a lot of physical exercise. Often kids that can't pay attention need more exercise. Most kids need more exercise. Especially in fresh air.
5. Also made sure she ate well.
Anyway, I found her at the end of four months to be a changed girl. In many ways.
In doing what you did, you used a creative and flexable approach, and such methods are almost never done in public schools.