When I talk to schools, I start by bring up DDs intelligence just as another fact about her (along with her weaknesses, challenges, interests, personality, etc.). I try to make an honest picture for them. Then I watch for several common responses:

* Ignore her characteristics. This is the biggest red flag for me. Because if they're not interested in discussing how the characteristics of my kid match their school, it's not the right match. Be careful though, some schools will fool you by telling you all about what you get for your money, making it sound like they care, but they aren't addressing YOUR kid.

* Ignore the LOG characteristic. If they talk about how they're a good fit for everything but the LOG, that's also an issue. Because it's a part of who she is and they are clearly uncomfortable about that or unable to deal with it.

* If they get defensive, uh oh. A lot of the statements in the OPs list sound quite defensive. Whether it's because they've been assaulted by special snowflake-itis or because they just have an entrenched attitude, the underlying messing is "don't question or challenge us."

* If they have a logical response of any kind (we do 'x' and here's why it works for us or here's how we handle intellectual diversity from both ends), that's good. It's good even if what they do isn't the perfect answer (what, your tiny private school doesn't have self-contained PG classes?). Because a) they are aware that kids come in different flavors of brightness and b) they've thought about what that means. I particularly appreciate when they talk about what they do for bright kids, but also talk about what they do to support kids across domains (bright, struggling, disorganized, emotional, social). A caring school that supports every kid should be able and willing to support your kid.

* If they tell you "we think she might be bored" or "we can't accommodate her" that's the easiest answer, because there's no BS and you can strike them off your list. I wish more schools would be so honest. I have heard both of these from schools I've talked to.

Frankly I'm not sure if the 'what do you do if a kid doesn't fit?' question is quite fair. The point of private school is that it's a choice, so there should be a good fit. I know that's unsatisfactory from a parent standpoint, but the school does have the right to say 'here's how we operate, will you be a cog in our machine or the squeaky wheel?'

We have two local privates, very highly regarded, that I know provide superb educations for many kids. However when I talked to them the attitude seemed to be "you need to go along to get along here" and "we are so awesome that there aren't ever any problems."