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:
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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.