Essentially the Z-coordinate of the Head Pose NBT data, rotates about a fixed reference frame (i.e. it relies on the Rotation NBT data tag to determine which way it rotates), whereas the X-coordinate rotates about the Y-coordinate, using that as its reference frame (i.e. it relies on the Y-coordinate Head Pose to determine which way it rotates)

You can play around and visualize the movement on this website (which mimics exactly how it behaves in-game): https://haselkern.com/Minecraft-ArmorStand/

Try setting the Y-coordinate of the Head to 270, and then sliding the X-coordinate which moves the head as expected, but the Z-coordinate moves the head along the same axis as the X-coordinate, instead of perpendicular to the X-coordinate rotation.

Proposed Solution

Make the Z-coordinate's reference frame be the Y-coordinate (so that both the X-coordinate and Z-coordinate use the same reference frame). This will result in the Z-coordinate being perpendicular to the X-coordinate.