Platypus, you're doing just fine!
Pinecroft, the additional evaluative methods for ADHD that haven't already been administered or mentioned would include some direct measures of attention not always available to school districts, due to their relatively high cost, such as computer-based measures (TOVA, IVA, CCPT, etc.). I also prefer multiple semi-structured classroom observations across settings, days, times of days, and tasks. This may or may not already be in the school record, and it may or may not be something a private neuropsych would be willing to do (although most professionals will consider it if you are willing to pay them at their hourly evaluation rate). You also may or may not get push back from the district about allowing an outside provider in the building for observations.
Generally, I do prefer to invest some time and energy into teasing out other factors (as mentioned and others: depression, anxiety, poor sleep hygiene, medication reactions, auditory processing, core weakness, vision, etc.), as children have a tendency to present as inattentive or restless for a pretty wide variety of underlying causes. It's a bit like acting out behaviors--without the developmental skills to identify, articulate, and manage challenges, they reach for the more limited pool of available communicative behaviors, such as "misbehavior", inattentiveness/disengagement, withdrawal, emotionality, angry outbursts. The symptoms/behaviors alone really tell us only that a child is distress, but not what the nature of that distress is.