To get buy-in from the teacher, you probably need to figure out what can be done within their offerings, i.e. ask for something that they can reasonably give you. Do you want her accelerated into a group at a higher grade level, for instance?
ITA. I'd also take advantage of the power of the "group" - you mentioned that you know other parents that have similar concerns - pulling your voices together toward a common goal that is something that can be accomplished within the bounds of limited school budget and limited teacher time to deal with will help you get closer to success.
I also realize this isn't going to be an ideal answer, but have you considered something after-school as an option? I realize that is essentially what you are already providing privately, but if there's a small group of talented musicians at school, would they be able to work together as a group one day a week before or after school (or whatever) if one or two parent volunteers sponsored and supervised them?
Just a few thoughts - good luck!
polarbear