Ah, Doitsu, thanks so much for the suggestion.
I had no idea control codes could survive in HTML. Not invisibly, anyway. I've done a test version of the epub, removing all but the one chapter where the problem occurs; it still happens. I then whittled that down, removing all text from the chapter except the ten or so logical pages before that point, and the remaining ten or so pages in the chapter after that point: the problem goes away.
With the copy of the chapter that has the problem, I've manually edited it in Sigil and removed all the spaces between the paragraphs; the problem hasn't gone away.
I'm really scratching my head with this.