Have you talked to the school about it trout? She might listen to her teacher's advice about how to handle an unexpected question more than she'll listen to yours. Also, you might want to make sure the school are aware that despite being super-bright, she's also inclined to anxiety and being a bit of a perfectionist, and might benefit from not doing any other early entry GCSEs - she is two full years young from the age they're intended for and she might be more mature and resillient by the time she is Y11. My eldest DSD has had panic attacks sometimes, though not really exam related. She learned the best way of coping with them herself and was able to tell others what she needed after she'd had a few and understood that they would pass.
My DD is a bit similar to yours and doesn't like to hand work in that isn't perfect. Actually setting her to talk to my (also similar to yours) DS is a good tactic - he's so laid back about things and tells DD she's being stressy sometimes which can help. I want to put the two of them in a blender sometimes, and produce a more balanced child 