I wrote a long response a minute ago but lost my connection and thus my post. So I'll rewrite a brief version.
ITA that a once-a-week pull-out is highly unlikely to address the other 6.5 hours a day your DD is in class. A pull-out can be fun and enriching, but it's not enough for most of our kiddos.
Glad to hear the GATE teacher is enthusiastic. Did you ask her if she'd be willing to bring both her enthusiasm and her admission that she can't do enough for your DD to your next meeting with the teacher and principal? Even if she doesn't have a ton of personal experience, perhaps she has some teacher-friendly research on acceleration (which is sounds like you want) and can explain any and all of your DD's testing results, particularly focusing on what makes your DD's case out of the ordinary.
Is your DD's school full of very bright kids making it harder to see that your DD is yet more unusual and has more unusual needs? Or does the school have a wide range of abilities that will make your DD's needs more obvious?
One thing that I found helpful in meetings with the principal and teachers is to acknowledge that budgets are tight and that teachers are stretched thin. Enrichment is difficult for teachers. Acceleration, however, be it subject or whole grade, is free and doesn't require extra work on the teacher's part. This argument shows them that you understand their challenges, and then you can work to all agree that she needs an appropriate education so that she can learn to learn.
Good luck with your next steps. But for now, ((HUGS))
