There are many ADHD "look alikes" and it is sometimes difficult to tease out what is causing the symptoms. Your evaluation is a good start - especially if it looks at academic skills, EF skills, language processing skills in addition to IQ.
I disagree that homeschooling is the only choice for a child with ADHD that cannot take medication. As you have noted, there are some supplements that can help, exercise has been shown to be a help, and schools must offer accommodations and supports to help students compensate for the affect (or is that effect) of ADHD. There are schools that specialize in teaching EF skills and they often provide a learning environment that is multi-sensory and structured so that the student can thrive. Some public schools offer explicit instruction in study skills, organization skills etc so that their students with ADHD can be successful. If needed, the law requires diagnosed students be afforded reasonable accommodations such as extra time.
I have one child that is gifted, has profound dyslexia and ADHD. When we first started out trying to understand him, I could not believe that ADHD could be part of the mix. He is calm, extremely well behaved and could sit still for hours when we went out to eat, working on art projects or spend hours playing in the woods. What I didn't realize is that because he became so distracted and entranced by things happening around him (ADHD), it looked like he was on task. Really, his mind drifted around constantly. And, when it comes to school work and chores, it takes him FOREVER to complete things. As it turns out, ADHD was part of the mix, and luckily, medication helps a lot.
For my daughter (not gifted), she has some processing and concentration issues, and we found that she has learned to compensate without medication. She worked with a tutor for a year that taught her how to study, organize, stay on task. We were able to secure a 504 plan at school that allows her extra time on tests. She went from a B/C student in college prep level classes to an A student in honors and AP classes without medication - just by learning the EF skills and by being given the time she needs to complete tasks.
If you are not already working with a medical doctor that specializes in ADHD, I would suggest that you seek one out. It is difficult to determine if a gifted child has ADHD or other challenge. A specialist will be able to analyze all the data and help you "peel back the onion" to help determine if it is more likely that your child has ADHD or another condition.
Good luck!
