Yes - totally agree.
Hun and Pennington are both good for kids needing support for LD. But I didn’t mention any NJ schools based on the OP’s list of preferred states. I think these 2 might require a bit more work to access non-school high-level music opportunities ( simply because there are so many day students who can access them without school support), but I really don’t know that for a fact.
We really need to understand where there is flexibility in the goals and where this family is on decision making.