I just read you said your DD is a prefectionist, so is mine. We often had the meltdown in the beginning and her saying she couldn't do it, she was going to fail etc. I think it was a symptom of if I don't try then I can't fail.
What I did was really try to stress that to do well we need to work hard and if she works hard and then doesn't do as well as she wanted, well thats okay. I tell her she can walk out of any test with her head held high if she tried her best.
I also told her if she was going to get angry or frustrated then it was time to quit and I was not helping her anymore. Once she got through the first few tests and got great grades on it, he confidence soared and we don't stuggle as much.
I tell my daughter this quote from Dick Vermeil " If you don't invest very much, then defeat doesn't hurt very much and winning is not very exciting."
We were struggling with my DD the perfectionist being afraid to try. And making mistakes. So we really don't praise on the grade but the effort she puts into things.