Making a note about a useful resource more than anything. This resource: https://craftatlas.co/natural-dyes/polish-cochineal gives some description of natural dyes, and while one could find more information on the “Polish cochineal” elsewhere, this one has an intriguing (though it’s hard to tell how accurate) color comparison of different natural dyes at the bottom of the page.
If it is indeed accurate, then one could claim that the shade of current Mexican cochineal is very close to the “Polish cochineal” traditionally harvested, sold and exported from Ukraine, unlike, for example, the “Armenian cochineal” – the closer relative of the Ukrainian bug, the shade of which is quite different.
Of course, even if this was an accurate reference point, it would still apply to fabrics and to the most generic/common recipes, since different shades and colors can be obtained from the same dyestuffs under different chemical conditions, and, of course, the colors sometimes work quite differently on eggs than on fabrics. Still, I thought this was interesting and wanted to save the reference.