Running short on time tonight, so just scanned the post and responses, so forgive me if I overlap with others...
There is more going on than ADHD.
While a comprehensive evaluation is probably called for, there are two other evaluations that you should get before the comprehensive. Before... because the comprehensive doesn't usually run these, but if they have been done, the comprehensive evaluator will make use of the results. Which gives you double-value for the evaluations...
1) Occupational Therapist (OT) evaluation for sensory and motor skills issues. Occupational Therapist (OT) cannot do dxes, but will provide detailed report, AND has therapies that help.
2) Speech Language Pathologist (SLP) evaluation for auditory issues - at 6, he's on the edge of "too young", especially if ADHD has been diagnosed and is not under control. However, APDs really do look exactly like ADHD in the classroom. Especially ADHD-inattentive. APDs can range from classical Central Auditory Processing Disorder (CAPD) where they have problems processing spoken language, to other more subtle APDs such as auditory figure ground, where hearing and language processing are normal but they can't filter out the background noise, so do not follow spoken instructions in noisy environments like a classroom.
For the record, both motor skills issues and auditory processing issues are highly co-morbid with ADHD. And that's on top of the fact that APDs can be mis-diagnosed as ADHD.