Robin, to modify your analogy, I always thought I was American. I mean, I thought I understood what Americans were saying, for the most part. I thought I got the culture, and that we were all using the same references.
Eventually, I started vacationing in France. I had always been interested in the culture, and had periodically owned/worn a beret, but I was shocked by how much more comfortable I was there. Not in an easily explainable way, but deep down, things were just easier. It felt like home. So I moved there.
While I was in the process of packing up my stuff in the US, I started talking more directly to my old American friends about culture. We had never really talked about it before; we all ASSUMED we were coming from the same place. Turns out we weren't, and that we couldn't have been more different. Turns out I was never American - I was always French.
So, I guess what I'd say is that you are not on a ship, lost at sea, being carried somewhere by forces unseen. You're already from somewhere, and your job is to hopefully figure out where that is before you die in a strange land, never having known home. Take ownership of your identity, and do whatever you can to figure it out.
If that's visiting every country in the world, great. If that's going to the place you always wanted to but could never afford or were scared of, do that. If that's buying an island and trying to start your own country, then good luck but you gotta try. Just remember that this doesn't average, and that there's a difference between identifying clearly as two things and identifying as something in-between. You can't create the experience of living in Kansas by spending half your time in LA and half in New York, no matter how often you make the flight.