Interesting that HP's magenta has a great deal more blue in it than Epson's.
The problem with using the standard color inks to offset carbon warmth is that the standard sets do not have a blue that is a direct complementary color to the carbon color. So, it's not a straight line pull (so to speak) by a single offsetting pigment. If it were, the fade path would be a much more ideal straight line to carbon warm. I did find a pigment that was the right color -- Danial Smith's Indanthrone blue. I actually did print with it, but I do not have the equipment to properly prepare pigments for inkjet printing. The volume needed for a company to do so was such that Zeiss (the MIS founder) did not think it made economic sense to do it.
Paul