What are good periodic color scales for density plots of angle-like function values?
As you note, there are problems with the typical rainbow colour map.

Kovesi has done some work on perceptually uniform colour maps. Code is available here: https://peterkovesi.com/projects/colourmaps/index.html

In my work, I replaced the rainbow map with the Kovesi's first cyclic colour map for the angle values, and used either saturation or intensity (multiplication) for the modulus. In hindsight, it would probably make sense to map the raw modulus values to saturation / intensity using one of the perceptually uniform greyscale linear maps as well.