Insert 2 pages after page 5.
Drag everything on Spread (before) 6-7 up to the new spread.
Delete the old spread.
Save as IDML.
Open the IDML and save with a new name.
Work with the new file.
Thanks for your help, everyone. Fortunately just the IDML export healed it - Eugene's suggestion would have been a huge amount of work (I have several master spreads, styles of all three kinds organized carefully in groups, etc.), and even Willi's wouldn't have been trivial, as that page had master page items that had been overridden (but that was going to be the next thing I'd try if Peter's simple idea hadn't worked).
Unfortunately, the IDML export was not perfect - it screwed up the use of a PDF that contained several ads. After the IDML roundtrip, all links to different pages of that PDF suddenly showed the first page (i.e. one ad) over and over, instead of the appropriate ad for where each was placed. To avoid that happening again if I have to do the IDML shuffle in the future, I split the PDF into separate pages and then placed each in the right location. I thought I would mention it here - IDML won't necessarily keep everything about your document just as it was, so be sure to check it carefully afterwards. But I'm glad it solved my mystery problem!
No work at all. The master pages would have transferred fine.
The IDML didn't screw up, it fixed. Obv the PDF pages had come slightly undone (corrupt).
Glad it's sorted though. I do feel my method would have fixed your ailments.