Note: the story below is fictional, but the legal question posed is a serious hypothetical.
While attempting to sail across the Pacific I discovered I was pregnant. Eventually I ran aground on the Palmyra Atoll and gave birth to a healthy baby girl. Obviously I have a lot to worry about, being stranded on a tiny uninhabited island with a newborn and all (yes I have Internet access don't think about it), but what really matters to me right now is that my daughter will be a U.S. citizen.
After all, I happen to know that the Atoll is the only incorporated, unorganized territory of the United States, and "incorporated" means that the Constitution applies in its entirety, so by the 14th amendment she should be granted citizenship by birth. I am not a U.S. citizen, so she cannot derive citizenship from me.
Now, how should I go about getting her stateside and proving to the U.S. authorities that she is entitled to citizenship? Should I sail to Kiribati and register her birth certificate with the authorities there, or make the longer trip to Hawaii and ruin my chances of ever crossing the Pacific?
You may assume that I have all the evidence necessary that she was born on the Palmyra Atoll. Before she was born, I had enough time to set up a camera and film myself measuring my latitude and longitude and then giving birth