I am no expert on the test scores but some of the behaviors you are describing sound very familiar. Your first paragraph could have described our son at a similar age. Please do not be offended at my questions, I don't mean any:)
First, is your daughter in any physical activities? We found that with enough (alot more than you'd expect) physical activity, DS is able to control most of these behaviors with a little reinforcement. At her age we were doing karate 4-5 times a week and running for 20-30 minutes a day before school.
Second, have you tried sensory products like weighted vests, fidget tools, etc? For 3rd grade DS sat on a balance ball at his desk in school. The result of falling off was having to use the regular chair for the next lesson period. He quickly learned to stay on the ball which gave him alot of sensory imput as well as an outlet for the fidgets in class.
The behaviors you describe can have many causes:) My experience has been try something, if it helps great, if not try something else:) The sensory processing products have helped us tremendously. You may want to look into this website.
http://www.sensory-processing-disorder.com/Good luck!
