Dan, 5J

And, as to landing at a port of entry to clear customs, I'd bet that's
only required if you intend to land in the country, not fly over it.

My understanding is the same; there is a difference between 'entering the U..S.' and 'flying in U.S. airspace'.
International airports are good examples to represent these two concepts: "The international zone in an international airport is the area where arriving international passengers have not formally entered the country by clearing arrival customs and immigration controls" - but they flew through the airspace, for sure.