I think a private evaluation would help a lot -
1) Give you some peace of mind
2) Give you some guidance
3) Give the school some guidance.
Remember that it doesn't matter what they call the intervention they do for your child - they could call it gifted programing or Apple Pie programing - you child needs to be in a classroom where the learning fits her ready-to-learn level. You want her to develop good learning work ethic, so she has to have lots of chances to engage with learning material that represents 'enough' of a challenge.
Let us know how it goes!
Grinity