Thinking about this more , you probably want this to develop a curve in your color space that represents something with constant CMYK values for your chosen light source.
E.g. your sodium light is 100% yellow, 10ish % magenta. Any color that varies cyan from 0%-100% and black from 0%-100% should presumably not reflect any additional color information (since the source light doesn’t have any cyan and black is just giving brightness)
I also think this means that as long as you hold Y and M constant, you can vary cyan and black for your comparison colors that will look the same. If you try to vary cyan and yellow or magenta at the same time then your effect probably won’t work.
This is tricky because you have multiple curves in the color space that are valid when just considering a single wavelength. The reality is, your lamp emits a spectrum of light (sharp, but still has a width). There’s also the variability in perception. But I’m not sure what the “bandwidth” of our eyes is and what color resolution humans are capable of detecting.