You are wise to be aware of the warning signs you are seeing and stay on top of them.
As far as options go... my top pick is home school.
We did hour away gifted with an only child. It was very hard but possible. I usually spent 4-5hrs in the car daily and drove 500 miles a week. With another child... I'm not sure we could have done it. With homework outside of school and extracurriculars outside of school offerings it would have been impossible. The school itself was only a good fit for one year. Different teacher made a totally different environment.
With homeschool there is always the ability to change if it just doesn't work. Public HAS to take you back if you change your mind at any time. It's a no risk trial.
At private schools most require tuition commitments. If it doesn't go well or something changes, if they totally lie about what they will do for and with your child, you still owe ALL the tuition.... even if the school is destroyed in a natural disaster. I haven't seen a private yet without those types of clauses in the tuition agreements.
Personally, I was convinced I couldn't survive home schooling my child and I had to explore all possible options before I tried it. He is intense and always doing something, he's never quiet, and won't be in a different room alone, he constantly wants to be in physical contact with me, he melts down with any pencil activities, and he gets STUCK like cement on ideas and things he wants... and my husband had just moved out so it was all me all the time. I thought my mental health was at risk if I lost the hours of freedom and quiet that school was providing. So I really understand concern about doing this with a 2e kid. And truthfully I absolutely never WANTED to home school. I know lots of home schoolers including my MIL and my husband and I were generally against it as an option in our family. It was something we had talked at length about over the years.
Having said that however, actually doing home schooling has been wonderful. There is much more peace in my life without school dramas and dealing with the every day aftermath of who my child was after spending those hours there. I'm no longer fighting "their" battles of getting him to do the ridiculously too easy assignments they piled on for homework or forcing him to go there every day or trying to get THEM to do what he needs. I've effectively fired the middle man.
My son is much more enjoyable to spend time with since he now has loads of free time to explore on his own after he finishes his home school work for the day and he isn't getting put through the wringer of a bad fit environment. I'm also getting the opportunity to find solutions to the 2e shut downs myself and teach him the skills he needs to be successful on his course ahead wherever it may lead. I feel this has been invaluable and timely. To hit his academic level he needs these skills right away. With those in place, we have more options for school choices should we want to change.
I sure hope you find a good fit for your son and family. It is certainly priceless and worth the effort to get.