Your post strikes a cord with me because I have 3 daughters who might someday have similar issues. My wife and I have made every effort to make sure that they speak the language and understand as much Japanese culture as possible, and although they go to Japan every summer to attend Japanese school, I think they identify themselves as "Americans".
While I lived in Japan I had a friend from Hawaii who was genetically Japanese, but was really hawaiian in every other way. He (while looking Japanese) spoke no Japanese. I on the other hand have blonde hair blue eyes, and yet can speak Japanese (at least I like to think I can) Sometimes when we were together in Japan we would go into a store and I would talk to a clerk (in Japanese) and the clerk would carry on a conversation looking at Mark while he never uttered a sound. It was like they were more comfortable looking at him while talking to me. It used to drive Mark crazy, he struggled to learn the language, but felt like everyone expected him to pick it up by magic, while if I someone who didn't look Japanese managed to string together a 3 word sentence the Japanese would be so impressed and praise the gaijin for his intelligence and hard work.
I think if you really have a desire to learn about your heritage, that you will find yourself frustrated at times. However I'm sure that the positive end rewards from such an undertaking will far outway the frustrations. Of course you will feel like a stranger at times after all you really are, no matter how you look, you're as American as anybody. You just might have the opportunity to learn about another culture from a more personal stand than those like me who have no genetic tie to Japan.
I wish you luck.