I solved it. The problem was that importing the Philippines zones from the file I got in the free add-ons section zorched my database and broke zone definition subzones. I did a clean reinstall of Zen Cart (1.3.9f) and manually entered all the zones I'll need. I guess the moral is: be careful of doing direct database importations to "save time". The more haste, the less speed.

Next time I set up a Zen Cart store, if I ever do so again, the first thing I'll do is set up countries and zones, by hand. Then I'll configure the store, then the categories, add some test products, configure and test payment and shipping modules, then do the theme last. That's the way I'll (re)do my store now.