Big red flags all over the place in your story and I am so sorry you are having this experience.
You are correct that your son needs appropriate work for his level or his focus will not improve. It is aggravating to here that Even if he does jump through the hoops they set and meet their standards, that will lead to more hoops and more of the same.
I cringe when I hear the "everyone has gifts, everyone is talented" phrase. I have been told that and I am sorry, all people have value but they are not all gifted and talented in an academic sense. They can't be or the curve of individual variation in intelligence would not exist. And it simply is not the reality of experience.
There is a lot of research that negates any value in repeating a child at school so the comment about "if that was my son I would make him repeat" is not supported in my view, particularly if you have evidence of his ability in academics and relationships outside the school environment.
Why does the psychologist think he should stay in an unproductive environment? I can't imagine there is any value in the experience when he is not understood by the staff and no accommodations are being offered. Different story if the environment is poor out of ignorance but there is some willingness to improve it if you can educate people.
I would move, as soon as possible, for your sake and your DS IF you have that option and the emotional and physical energy to achieve it. I know they can be big IFs.
Depending on where you are there may be processes to follow to organise support for giftedness or special needs, like the SPD,but from reading here, they can take time and energy to implement. When does your school year start and finish? Do you have many months in this current setting to make it worth battling for accommodations? Do your research into the school and the state's gifted policies, if any. Is there anyone at the school or in the school district that you can talk to?
I am no expert in SPD, there are others on the forum you can give you insights into how that is impacting and some advice on managing those impacts. Depending on his particular sensitivities there may be adjustments that can be made to the environment that will help with improving focus or therapies to explore. But at the end of the day, if lack of appropriately challenging work persists, you still have to deal with that problem.
Once children become unhappy and unmotivated it has broader impacts on them and the family so you are right to be concerned and consider all your options.
The good news is that the right educational setting, whether you create it where you are or move or go to home schooling, can make a big difference in a short space of time. I know the concern about the wrong environment "damaging" your child. Take heart, kids are very resilient and bounce back fast when the situation changes for the better.
We do want our kids to be happy. I wish schools would realise that is our prime concern and part of happiness is the right level of academic challenge and appropriate supports for any LDs.
