I know a psychologist who focuses on this population. Had the opportunity to occasionally pick up an assessment case or two from the practice. While there isn't a ton of referrals, these private schools cost $20-40K a year (high school). I was amazed one time a parent showed up with an envelope of cash to "just pay in full from the start" for , I think a $5,500 evaluation. And that wasn't even the most expensive option.
But you have to have tough skin while also having a keen ability to read the room and present your findings in a way that are accurate but also "agreeable." The nuances in wording and presenting results is something you notice real quickly with this population if you chose the "wrong" way to phrase it. Same with if there's a waiting list or any kind of delay. Many of these parents are CEOs, business owners, other top level "corporate types." Some tend to treat the psychologist like another person on their payroll. Sadly there's also a "fix this problem" mentality too; sometimes you discover a big factor in the poor kid or teen's presenting problem is the "throw money at the problem parenting."