Ultramarina - all of your second para applies to my HG+ ADD girl. She's a bundle of contradictions fiesty, opinionated, stubborn (INSANELY stubborn), loud, verbal, great questions, amazing observations and yet also a pixie and sometimes almost mute. We NEVER would have even considered that she could have ADD were it not for my researching myself to death with regards to her much more overtly 2e older sister. I have no idea what's going on with your DD, poor teacher fit, boredom, nothing at all... Just saying that I have a child that almost no-one would peg as having ADD (well not yet anyway, it could have been coming) who is vastly better off on medication.
Having moved on from being horrified at the idea of an ADHD diagnosis when considering my elder child, it was surprisingly easy to look at this child and go "Well it's not overt, but the tell tale signs are all there, lets get a professional opinion before it trips her over".