Nope, didn't have any effect.
All Print and Export commands are for the book, not individual chapter files.
Trial 1:
Opened the afbook file, and opened the chapter files.
Running headers are displayed correctly.
Saved chapter files, then saved the afbook file.
Closed all files, including the afbook file.
Opened afbook file, no chapter files open, Export “All Chapters as Pages” PDF/X-1a:2003
The output PDF showed the <Running Header> at the top of every page.
Trial 2:
Opened ONE chapter file with a running header, confirmed it displays correctly.
Export with same settings.
Running headers are correct for the chapter that was open, still wrong for the other chapters.
Trial 3:
Closed all files again.
Selected Book > Print, > Save as PDF using the Mac default PDF driver
All headers are wrong, and the page size has been changed to A4 with the text block centered
Trial 4:
Same as Trial 2, using “Save as PDF” option
Same results as Trial 2
Trial 5:
No Chapters open,
Print > PDF > Open in Preview
All headers wrong
Trial 6:
One chapter open
Same results as Trial 2
Trial 7
No chapters open.
Print > “Save as Adobe PDF” using Adobe CC driver
All running headers wrong
I have a few more options I could try but it seems pretty cler that either (1) this Mac has a problem (possible but unlikely, since PDF output from Adobe and other software works normally), (2) there's some weird collision between Publisher and something running on my system, or (3) Publisher has a problem.