Recently a friend asked me to recommend something for his rambunctious 4th grader. She also craves movement and crashing into stuff. Her teacher notes that she wiggles non-stop in class.
I am a huge fan and advocate for martial arts. But not all martial arts offer the same experience. It's good to consider what your student (or you) will most benefit from. In our area there are multiple types of martial arts; Ninjutsu, Akido, Tae Kwon Do, Karate, Folk-style Wrestling (America's Martial Art!) Jujutsu, and Brazilian Ju-jiutsu just to name a few.
None of these distinctions make a school good or bad, but they are simple distinctions which may better suit a specific student.
I'm also a fan of Folk-style or collegiate wrestling. This involves a lot
of physical contact, short moves to learn, competition, and self discipline.
A final consideration, parents may find it useful to talk with the staff and ask specific questions: i.e.: is your school comfortable working with kids with _______ (autism, Aspergar, sensory issues, or some other consideration). Some will be uncomfortable, others will jump at the opportunity to help your child reach his or her potential. Go where the staff are excited to work with your child.