I would answer the original question with an affirmative whenever the parent's concerns are divorced from reality, whether imagined or exaggerated. Since your concerns seem to come from a very solid foundation, any "pushing" you do is perfectly reasonable, because in this case the resistance is the irrational response. They call these kids "exceptional" for a reason... they are the exception to the rule, and need to be provided for differently.
In dealing with bureaucracies, it's very common for the person in charge to initially resist. But since the new director knows nothing about your son, it's her reaction that is irrational, not yours.
Give her credit for not dismissing the option out of hand, though. If your child is who you think he is, then he should show he can handle it in a six week trial.
Often times what is best for the large group is the structure of the traditional age-graded classroom without a lot of deviation.
That setup doesn't really benefit the group. It's set up to benefit the teacher.
