There are many routes to take. I understand your feeling of no meds, I felt that way once also. I am a mother of a child who was diagnosed with ADHD & who was on medication for 5 years, we have been through alot. He is now 12 and off meds.
First, you should get your child tested. That does not mean you need to put him on medication. That means you will know what you are dealing with, and know how better to treat the situation. You can try changing the diet, using behavioral techniques, and if those don't work you're left with meds. Pyschologists can be a big help in the behavioral techniques area.
Personally I think it is irresponsible not to deal with these issues. It will hurt your child in the long run. This means lots of conferences with the teachers and working with them. My experience is that works a whole lot better than fighting them. That does not mean meds vs no meds - but things like behavior contracts and following up on them. Also, kids like this, do get picked on (by kids and sometimes teachers). These kids social skills are not as good as other kids. It is imperative that you stay involved - its time consuming but very worth it. The child needs to understand about his behaviors, what is acceptable and what isn't. As they grow up, they learn more slowly than others, but they do learn.
BTW - the TV thing is hogwash.. my child was this way from day 1. I remember see is eyes dart back & forth as a baby and being on "high alert" at 2 months old. Other babies at that age, were not like that. Oh & these kids are highly intelligent - but they just need some help learning to deal with their overactive mind that isn't working the way it should. So, lots of love and understanding is very important. Also, they need structure. The busy lifestyle you describe could be making it worse for him also.
Take care & good luck!!