I'm showing how to emulate PM using additive oscillators and distortion/waveshaping.

The math behind this matches how PM works.
Phase modulation adds the output of the modulating signal to the phase (input) of the carrier signal, like this:
S_output(time) = A_carrier * S_carrier(time * ω_carrier + ɸ_carrier + ModIdx * S_modulator(time * ω_modulator + ɸ_modulator))

The input to the carrier is a sum of: constant carrier phase, time * frequency of the carrier, which can be thought of as a saw wave of said frequency, and modulator output, which can be any signal we want to modulate with.
On the other hand, waveshaping distortion works like this:
S_output(time) = A_post * S_curve(A_pre * S_input(time))

The input signal is multiplied by the pregain, passed through the curve, and amplified by postgain. If we match the waveshaping curve with the shape of the carrier signal, we can emulate Phase Modulation. If we want multistage PM (O1 modulates O2 modulates O3, etc.), we can just attach multiple waveshapers in series, combining inputs to match modulations.