I don't think you are missing anything

to mirror a positive waveform to a negative waveform a standard inverter would absolutely do

for the phase offset a short dc coupled delay would work - but if the frequency of the waveform changes the so will the phase offset - so may not be a viable solution

"some of the best base-level info to remember can be found in Jim's sigfile" @Lugia

Utility modules are the dull polish that makes the shiny modules actually shine!!!

sound sources < sound modifiers < modulation sources < utilities