Thanks for taking a look, BigLug. I'm afraid the results are the same, even if I use translate to move the text about. Note that there's no problem creating new PDFs, e.g. if I use PDF::API2->new instead of open, and page instead of openpage. If I do that, I get a nice big "Wahoo!" exactly where I expect it, so I know it's not a problem with fonts, or the geometry. But I've had no luck whatsoever in modifying existing PDFs.

FWIW, $PDF::API2::VERSION is 1.081.