But my head moves. And I saw the nodes on the spectrum graph moving pretty significantly when I was moving the microphone short distances (just a few inches).
Yes, you can't solve the problem perfectly. It's just the best you can do, that's all. Inside a perfect resonator there are positions where no increase in input power will result in perceived volume increase. Fortunately, car interiors are extremely imperfect resonators.

Or perhaps just averaging four runs, one each with the balance and fader cranked in each direction.
No, you said that before, and I disagreed for a reason . Changing balance and fader controls only simulates "moving the soundstage" if you ignore reflection effects, and node hunting is all about the reflection effects.

Peter