I finally got a pin properly inserted to secure the last brake pad - the other three pins went in pretty easy, but for some reason the fourth pad gave me some fight. What seemed to be the problem - there's a mold seam that runs right through the the middle of the pad, down the long way. At the nose of the pad, the part that gets inserted first into the holder, that seam prevented the nose from running all the way up into the closed end of the holder. It was probably just 0.2 mm or so short of being fully inserted, but that was enough to prevent the pin from being able to fit through that bottom hole. I scraped that mold seam clear up at the nose of the pad and reinserted it... now the pad went in just that little bit more, and the pin could find its way out the bottom hole.
details, details!