Okay, so the idea with the normal map was actually quite helpful. The u- and v-directions follow the texture u and v, which is quite nicely visualized by putting a tile pattern on lo-res Antonia, making a subd morph with a constant delta of either [0.0 0.01 0.0] (u-direction) or [0.0 0.0 0.01] (v-direction) and playing with the dials.

-- I'm not mad at you, just Westphalian.