the full name of the country is the United States of America, hence the short-form "Americans" to refer to the citizenry.

Yes, that certainly seems a logical enough explanation as to how the word ‘American’ came to be accepted as meaning ‘a citizen, or the citizens, of the United States’, but, having recognized that possibility, doesn’t remedy the problem of the word lacking exclusivity for the citizenry of the U.S. As I mentioned above, citizens of the U.S. are Americans, but so are all other citizens of the American continent, just as the citizens of Morocco, South Africa, Somalia, Senegal, Chad, Egypt, Angola, Gabon, and Tanzania are all Africans.

You’re right; there is no confusion, only the absence of a word that exclusively describes the citizenry of the United States.

Your suggestion of ‘U.S. Americans’ seems less unwieldy than ‘United Statesians,’ or using, as you wrote, the full name of the country, ‘United Statesians of America’. It is the best suggestion so far.