I don't know. I think evaluation outside of school will be expensive and yield little results especially since jdsf stated they are not interested in testing. I am not really seeing the ADHD except some with the memory, but is not enough to impair her, if it is adhd. Maybe enroll her in a martial arts program or an exercise program. Both are good form of natural treatment for ADHD and are great for kids with out ADHD, too.
It seems that it is impairing her to some degree.
It's more expensive than a typical co-pay but an evaluation at a hospital based clinic is around $300, depending on how one's insurance works. Schools often get it wrong, particularly with more subtle issues that seem like "obvious" instances of laziness or lack of will power. ADHD symptoms are shared with other diagnoses, so it is possible that it isn't the problem. School evaluations for ADHD tend to focus on symptoms of hyperactivity, using an evaluation like Conners which isn't useful in identifying ADHD-PI. And though ADHDers benefit from exercise to some degree like everyone else, it isn't a "treatment" for ADHD.