A previous HN thread had a lot of people comparing ADHD to the effect of chronic sleep debt, with the suggestion that ADHD could be an effect of the inability to enter deep sleep. "Like never having slept enough" isn't an analogy I would make for my symptoms, but it would seem to fit yours much more closely.
As a probing guess, are your symptoms helped more by NRI-class drugs? From what I know about norepinephrine, it governs whether moment-to-moment attention will tend to fixate or drift. The symptoms of both that, and the disorder of motivation, seem to get conflated as "ADHD" for some reason.