Montessori has its advantages but in your shoes, I'd dig deep into the school's curriculum. Maria Montessori lived many decades ago and the world has changed a lot and we now know a lot more about how children's cognitive development than they did back then. Who exactly is in charge of the school's curriculum and how it is being developed? How can they meet the needs of a gifted learner?
I do like project-based learning in theory but in practice, it'd take an amazingly gifted teacher to make that work in a classroom with 20+ children. Your child would need an extraordinary amount of luck to have such a teacher year after year.
STEM school...I'm not so sure about that option. A lot depends on the school culture. One of the private schools we applied for DD is STEM heavy but by the end of the school tour, I started to wonder if it's better to send DD to all girls' school that has a STEM focus since I saw zero girls in their advanced STEM classes.
