You also mention that she erupts when she feels inadequate or in trouble. And you mention she responds well to positive reinforcement. I would suggest the school try to keep track of the situations when she feels inadequate, and then try to cue your daughter in advance to prevent her from feeling inadequate. For example, if the teacher's tone becomes somewhat negative if your daughter is not keeping up in some way or if your daughter is slow to make transitions from one activity to the next, what I would suggest is that the teacher (or an aide) cue her a few minutes in advance when a transition will occur. It might also help to include a comment like "you've done a good job" or "you don't have to finish today" if your child is worried about her performance on a given task. Encouragement and less pressure sounds like it would work better than negative consequences.
In addition, you and the teachers could help your daughter recognize areas of competence, if you are not already doing this. If academic areas are stressful for your child, maybe she would enjoy an extracurricular activity, such as a sport, music, or art. Again you may already be doing this, but continue to find areas of success for your daughter to help compensate for feelings she has of inadequacy.