I've been reading up on diet.
Elimination of artificial colors and sodium benzoate seems to make a significant difference for a minority of children. This is about the only diet thing that has been confirmed by reputable science. If you kid is in that minority elimination of these substances is about one half to one third as effective as Ritalin without side effects.
Omega 3 and 6 might be helpful and might not, can't hurt to eat fish twice a week. Studies are being done but the studies so far aren't conclusive.
There are a bunch of hard to follow diets which have been studied none of which seem to have as much efficacy as gypsies curses.
Parents have reported amazing improvements in their child's behavior under strict regiments of placebos. Clinical analysis reports no observable change in the kids behavior but the parents think it is a stone cold miracle.
It seems that a little caffeine can help which makes some sense to me. If you are low on dopamine and caffeine makes it a little easier for those neurons to fire it could be a mild boon.
The other thing my reading has convinced me of is that there are parenting techniques that can help kids develop effective self regulation. Parental training is the most effective non-drug intervention. It's probably the most work.
My mind has been blown by what I'm reading. I realize now that I was an ADHD kid. My mother and my teachers at school did a super shitty job of dealing with it. Punishments were often a tad sadistic, like being grounded for an entire school year (not allowed to go to friends houses, have friends over or watch TV). Take a kid who is acting out because he is, for one of a few reasons dopamine staved and crave stimulus, remove a bunch of stimulus as punishment, and watch they act worse than before. This was my life in a nutshell. Lot of other dark bits related to all this and other unrelated dark family shit, not exactly happy childhood. Luckily I found books and checked out of the real world that hated me for who I was. They got me through high school and out of my house so I could find out who I was after being harshly poked at for a dozen years.
Each generation of my family has treated their offspring significantly better than the one before it. This is my time. I'm not going to let anyone grind my daughter down and at the same time I'm going to do my best to help her be a happy and effective person who takes responsibility for her behaviors in the world at large.