I assume that you're putting "correct" in quotes because you disagree with the idea that this is correct.
> The mathematics of harmonious color are fairly well understood...
Disagree. Human perception of color is highly nonlinear and we are constantly inventing new color spaces as tools to understand human color perception. These color spaces all have various tradeoffs and limitations. While useful, it's clear that our understanding is very limited.
> Lab is a wonderful scene referred color space, but suffers from mathematical complexities that disables simple mathematical operations. The reason is that shifting a hue, for example, may describe a color that simply does not exist. (Think of it as divide by zero, but for colors.)
(Note: Color spaces are neither "scene referred" or "display referred", so it is incorrect to call Lab "scene referred".)
This is true of various RGB color models as well. It is not unique to Lab. Many color models have this property because of the overlap between different receptor responses in the eye... it is fiendishly difficult to figure out a way to represent perceptible colors without including imaginary colors.
My conclusion here is that the only reasonable way to teach people how to pick harmonious colors is to have real humans use their brains and sense of aesthetics. Mathematical models for color perception tend to be either poorly suited for this task, or difficult to work with.