One thing I’m curious about is how you would define your “specific portions of the gamuts that jut out” and more importantly, how would you delineate where the exact areas you’re interested in finding the “difference between the two gamuts for each specific area of mismatch” start and finish?
As an example, consider AdobeRGB and Epson SP3880 Premium Luster profiles - in the screenshot, you can see that the 3880 profile extends outside of the AdobeRGB profile in the bright(ish) yellows and also in the blue/magenta/purple 3/4 tone areas. But how exactly would it be possible to say where the start and end of the area is, which juts out?
I’m not sure I understand exactly what you mean when you say “not to mention the huge number outside the LAB gamut” when referring to colours in the ProPhotoRGB gamut. An ICC profile is essentially bounded by the Lab gamut/space, so how could any profile actually represent anything which is beyond the Lab gamut? Is it even possible for any colour to be outside the Lab gamut? There are definitely colours which can easily be represented by a Lab co-ordinate but which are absolutely imaginary and not at all possible in the real world or for any human to ever be able to not only see but not even possible to visualise or imagine.
Something like 0,128,0 or 0,0,128 are complete nonsense, really. How could anyone ever even comprehend a colour which is darker than any black ever imagined yet at the same time, a more intensely saturated red than any laser could ever hope to produce? Or a yellow, again more intense than anything in existence but simultaneously as dark as dark gets - the absolute absence of any light is what L=0 is representing.
But I’m just curious about those colours in ProPhoto which you mention are outside of the Lab gamut. Please explain