"Julian Scarfe" wrote:

So the next question, which I'll ask on Peter's behalf is...

Since Part 97 only prescribes approaches for airports within the US (and
presumably associated territories), how does an N-registered aircraft ever
fly an IAP in IMC outside the US?

That's easy, this rule doesn't apply outside the US. Part 91.1 says:

"this part prescribes rules governing the operation of aircraft [...]
within the United States, including the waters within 3 nautical miles of
the U.S. coast."