Huh, this is the easiest suggestion yet. I'll try that!

And I think I just put two-and-two together about something: when I go for long rides, I wear the rigid MTB race shoes. These have a considerably higher sole profile and raise me further from pedal center than the BMX shoes that I use for my daily commute -- effectively, they lengthen the distance from my knee to the cleat. The saddle feels noticeably "lower" when I wear these shoes, yet I have not bothered raising the saddle to compensate. Well, now I will, and we'll see what happens...