I've been studying color theory (its harder than you would think) on my spare time; and I did my undergraduate thesis was on posit few years ago. I think using posits may be a good idea to compress the luminosity, but I'm not sure how good it would be for the ab on a Lab-like format.

A format close to the cone fundamentals, like XYZ, could have benefits being encoded in some kind of non-standart posit.

I'll add this into the stack of things I eventually I'll look into.