Possibly you needed to taper the ambien much more slowly than what your doctor recommended. In my personal experience, doctors tend to underestimate how dependent the brain gets on psychoactive medications. The other thing you might be experiencing, besides prolonged withdrawal from ambien, is whatever sleep problem you had in the first place that caused you to get on the ambien. That part, the sleep study might be able to identify. Good luck.
If you figure out how one can get by on 2 hours sleep, patent it and sell it, you'll be rich. The world is full of people who want more time each day and think sleeping is a waste of time, but they keep falling asleep... and need it.
You condition seems a contradiction. Not sure how a sleep study will help. My experience there is the study measures how much REM sleep you get and if you are getting sufficient oxygen and have a reasonable heart rate.. maybe a few other things...but nothing that would explain why you are never tired.. unless it shows you are really sleeping 7 or 8 hours and just don't believe it.
Good luck.