The three signals from the oscillator section, A, B, and C, feed into a clock phase generator section. The three signals are converted into four. Here's the logical diagram:
So how was I able to get the timing of each phase? It turns out that pin 1, not connected on the PCB, is the B_XNOR_C signal. I measured that in relation to the A signal on pin 2, and so all clock phase periods are known.