ranging from just keeping hard-coded strings containing the expected output, up to and including implementing our own fake versions of external infrastructure.

This sounds very familiar, we rely on external credit systems pretty heavily. We started by mocking service responses and including the response XML in our unit tests. Now we have a service simulator that returns expected values and has record/playback capability. It's not ideal and responses get outdated occasionally but we haven't found a more elegant way to handle it yet.