I think it's worth poking the school to get their explanation of exactly why your child wasn't selected for GT. I don't know of any school system that only accepts children with a 99th percentile CoGAT (or similar), unless there are some other weaknesses. When schools have these programs, they tend to cast a wide net.
Also, be quick to point out this:
Her teacher says she does not participate in class. When I ask her about it, she says her ideas are so different from the other kids that she is afraid to share them.
Because that says GIFTED.