Except. It turns out that the rails from the ceiling to the garage door opener were maybe an inch off plumb, which means that there might have been as much as two or three pounds pulling on those nails. That, plus the vibration of the opener, plus the vertical loads when the door is almost closed, was apparently enough over the course of a few years.
So I cut off the nails (thank you, fencing tool), zapped in 8 or 10 long screws with the baby impact driver, and away we went. It would have been sort of embarrassing to call daycare and say we couldn't pick C up because the garage door was jammed...