Your child is lucky to have a parent like you.
A similar dilemma presented itself when I was 7 years old.
This was 1968. There was a teacher's strike. I was in a public school class with kids with all sorts of disabilities. Fortunately, in retrospect, I realized that the teacher understood my needs. She would yell at me--but she would provide me with "advanced" books to read.
But my parents felt like they needed a private school for me--so they enrolled me at the Summit School in Queens. It used to be located in Forest Hills. Now it's located at about 188th St and Grand Central Parkway. It was for a wide gamut of "disorders" then. However, they placed me in the proper class--for "smart" kids with emotional disorders.
It was a rather strict school then--and it still seems to be strict today. I didn't know it then---but it did provide me with a good academic basis---which helped me later on in my school career.
You should go visit it. They strongly emphasize academics. They might emphasize discipline a little too much, though.