Update:
The independent eval is complete and the psychiatrist said that my son is indeed twice exceptional and the school is not making enough accommodations for him to succeed in the long run. Because of that she wants to add a diagnosis of ADHD (which she said is stretching it but that the boredom he is experiencing at school is manifesting in inattentiveness where it's interfering with his work). She is hoping that this will force the school to take action. She also suggested getting in touch with an advocate (which I have) to help fight the school on his behalf.
Moving schools and homeschooling are not options at this point...I'm hoping we can come to a resolution that will help him overall. Thanks to everyone who have offered advice. If anyone still has advice on how to fight a school for an IEP/GIEP for a 2e child, I would appreciate it.