I still have a lot to learn about controlling cameras but have figured out that I never needed to point the Aux Revolving Camera at all, just parent it to a null object (in this case an invisible ball centered on my figure) to make it behave like the main camera revolving around the center of the universe.

Pointing it at the ball made the Dolly X and Y controls behave differently, which I countered by animating the ball itself. This worked the first time, but after changing the length of the animation there was a glitch where the view jumped vertically several pixels (the ball's Y translation, and camera yaw and pitch just had keyframes at the beginning and end). When I stopped the ball from moving the problem went away. Then I tried parenting the camera instead of pointing it, and was able to get the exact same camera move without the glitch.