She would like to skip another grade and go directly into 5th grade next year so that "maybe I can actually learn some new stuff at school" (her words). The problem we see with that is that while there could be more things in gr 5 that she doesn't know already, the pace at which she would pick it up is still going to be so fast that there is still a real possibility that she will be bored there too.
Cut it out Kerry honey!
Step away from the 'Perfectionist Edge.' If you feel like you are going in circles, then you know that your 'strong brain' has shut off and you are in 'fight or flight mode.' It happens to everyone, and we who don't have safe local peers are the most vulnerable.
You won't know if it will work until you cross that bridge. A full skip will help 'for a while' no matter what, and if there is luck, you DD may find a friend or two in 5th grade who is able to work at her level, and a teacher who 'gets' her.
The closer the child is to the 95% mark in the classroom, the easier it is for the teacher to differentiate, and the more likely it is to find social/academic friends.
If not then she may need subject acceleration - which are hard if you have to go to the next building for middle school, but even then, can be accomplished the following year. This is a marathon, and every step in the right direction brings relief. At "HG+" we say: If she can even get 6 months of learning/fitting in in a school setting you get to be delighted!
There are disadvantages in sending the message that your DD is 'so vulnerable' that she has to have her fit 'just EXACTLY right.' Getting improvement is what you want to aim for. Some kids are that vulnerable, and so carry on, but if your child isn't, it's best not to nudge her in that direction.
Just Make sure:
1) That 5th grade at the new school is more advanced than this year at the Magnet.
2) That you have sat and observed the new classroom and new teacher before you commit
3) That you keep encouraging DH to afterschool - you can call it 'getting to know her as a learner' and making video to document and demonstrate to the schools the 'DD difference' - a picture paints 1000 words.
4) keeping strong emotional bonds so that you and DH are places where DD can go to recharge.
Kids can usually be accommodated with a combination of full and subject acceleration, especially if they are fairly hardy souls, without 2E issues, if you can find a school that is willing to be flexible.
Good luck with the job search!