Thanks everyone for your replies! The reason that dental health is so important, important enough to force him to brush his teeth, is that he was born with a bilateral cleft lip and palate. After five surgeries to repair the structures in his mouth and on his face, we are now starting with the teeth. He will have to have a ton of orthodontia in the future and we can make all of it easier by ensuring that his teeth are the healthiest and cleanest they can possibly be. He already has an extra hidden tooth and his teeth are too close together, too. Anyway, just changing our diet and taking supplements, which work for some children, just isn't enough for him, but thanks for that perspective.
I will be trying all of the strategies everyone suggested over the next week or so. Yesterday, what seemed to work best was a new tooth brush that lights up, combined with letting him brush mommy and daddy's teeth while we brush his. He didn't cry!

Now, if we can just get him to do this while lying down, to be able to get to all of his teeth more easily and more completely!
Thanks, mamas!