This sounds like both my kids at this age, the wiredness, the fighting sleep, the never laying down on their own, the super early waking - and the answer was...brace yourself....dropping naps. With a nap, they would log between 8--9 hours total sleep per 24 hours. With no nap, they were up between 5:30-6am, but asleep by 7-ishpm, so an extra 2 hours. We just changed our evening schedule so that we ate at 5:30, and they were in bed by 6:30 - yes, they didn't see my husband a lot during that time period, but sleep was the PRIMARY OBJECTIVE at that point, and they bonded with him at other times (mornings, weekends). It was a short time frame (a year or so for each kid), and declining evening invitations to events/changing up our evening routine as worth it. They were both always early risers as toddler/preschoolers, and were always on the low end of sleep needs. It's ummmmm....tiring. To say the least. But I never thought of it as pathologic or something that needed to be diagnosed, just as something that needed to be managed and making changes in our routine and readjusting our expectations of "normal" was the key. FWIW, they are both very bright, very energetic, inquisitive kids who we are relatively sure inherited DH's ADD, and all of those things add up to kids who are not impressed with the beautiful dreamland that is sleep.
We figured this out when they were taking 7+ hours after their nap before they were able to fall asleep for the night(3pm nap wake, 10pm bedtime)...BUT also weren't ready for a nap until 7+ hours after they woke up (5:30am wakeup, 1pm nap). It was mathematically impossible for them to nap and log more than 8-9 hours a day.
I know kids are "supposed" to nap up through preschool and even into Kindy for some, but mine were done with naps at 26 and 28 months, respectively, because otherwise they got so little sleep they were a mess. Dropping naps for a 2-yo sounds crazy, but total net sleep increased remarkably in our house when we did. I won't say that the 4pm-7pm "witching hours" were pretty at first, because they were not - keeping a cranky toddler/preschooler awake but calm and not overstimulating them while trying to get dinner and bedtime done was challenging at first. But, through trial and error we figured out routines that helped it all work out.
They are 8 and 6 now, and just last year was when they started sleeping in routinely past 6:30am.
FWIW both of my kids have behavioral issues related to dairy, and artificial additives in foods. Wheat is also a culprit for a lot of people.