I'm not sure why this is so stressful. For one of my kids, I submitted the DYS application the same day I got scores and spent less than an hour on it. It's not that big of a deal, especially with scores that meet their criteria. Just fill it out!
I remember getting the initial big scores and freaking out a little. I sympathize. It's a lot to get your head around initially, but from a few years later down the road, the scores are far less interesting. Ultimately, kids need what they need from school and while there is some correlation with IQ, I've seen PG kids thrive or fail in virtually all circumstances. The IQ doesn't determine her needs or what will work for her.
Being admitted to DYS will not change your circumstances or make school administrators suddenly get it, or provide you a good school fit for your child. There is benefit in having access to other parents with similar children, but ultimately finding a good situation or a least-worst situation will be up to you.
One last caveat regarding extended scoring . . . . IQ tests simply are not that reliable in the tails. Extended scoring and very high FSIQ were based on extrapolations from very small numbers. Even in the pool for extended scoring, I think the highest regular IQ was 151 (IIRC?). These numbers are fairly wild extrapolations and should be taken fairly lightly. Your child is not a number and her educational needs are not fully determined by IQ. Some kids with FSIQ >150 manage fairly well in school with some accommodations or a focus on sports or a focus on ECs or social interests. Some struggle mightily in school even with far lower IQs. Some need early college to provide challenge. Some find better circumstances locally and make it work. The number itself tells you that your DD is wicked smart, but not much more than that and her personality, your options, and her interests will ultimately determine how her intelligence interacts with the world.
