Poking around on wikipedia (https://en.wikipedia.org/wiki/Compatible_Discrete_4), I learned that true four-channel quadraphonic sound, for LPs, was obtained by further recording two more signal streams in the same groove.

These other channels were recorded with FM (frequency modulation) on top of a 30 kHz carrier. The 30 kHz carrier was just high enough to isolate the quad channels from the 0-15 kHz ordinary left/right stereo channels.

And then, the FM portion, centered around 30 kHz, was added to the regular baseband audio signal (0-15 kHz), and all encoded into the diagonal displacements you mention in your comment.