It looks like you've got a good measure of what's going on now.
With regards to being "that parent," your child's scores sound like the kind of scores that will demand that you be "that parent." However, there are positive and negative ways to do it. First and foremost, don't have conversations about your child with the teacher in public! By that other parent discussing her concerns in front of others, it put the teacher in a position of not being able to say anything but "let's see how she does."
Make an appointment and treat the teachers respectfully as as the professionals they are, and being "that parent" isn't so much of an issue.
