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.
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.