First of all thanks for the comments and info.
I'm actually not doing the color interpolation myself. I'm using chroma.js[1] for the most part.
You can actually change the interpolation mode on the bottom below the color boxes. The default is LCH because I think it looks the best most of the time, but you can use LAB if you prefer that.
CIE L*C*h is based on either CIE 1976 L*a*b* or CIE 1976 L*u*v*, it's just a different representation. <--for formatting or the asterisks vanish.
For displays you're incrementally better off using LChuv. But note that these are very rudimentary color appearance models compared to CIECAM02 and newer, where surrounding color and ambient light can be taken into account. For a given color, surrounding it with two different colors will produce a different color appearance for that given color, i.e. a spot measurement of the given color will of course be the same, but the color in context will be different. It's a feature of human vision. Simultaneous contract, Bezold effect, and so on.
But without display compensation (mapping the CIE color created for given RGB value, such that a color management system can alter the RGB sent to the display in order to preserve color appearance) you will still have the experience of getting a different color for a given encoding on different displays.
How far down the rabbit hole do you want to go? In any case, these are better than HSL and HSV representations.
Really cool site! After playing with it for a while, could the CSS gradient for MIX could be changed to use the same number of color stops as there are steps rather than just using the start and end, to better match the chosen interpolation mode? I had a great gradient in LAB space, but the CSS version interpolates through ugly greys in RGB.
You can actually change the interpolation mode on the bottom below the color boxes. The default is LCH because I think it looks the best most of the time, but you can use LAB if you prefer that.
[1] https://gka.github.io/chroma.js/