Reading above, I was thinking of mordants, but someone mentioned. Different
mordants yield different colors out of the same dyes. Also, the container in which you do the dying gets involved in the mordanting process_same dye, same mordant, different pot (stainless steel, cast iron, copper) also yields
different colors. Also how long it sits in dye bath, temperature of dye bath,
when in the process dye bath is heated. Not as complicated as it sounds.
Google spinner's and weaver's guild for your area, or talk to native weavers.
They'll happily share standard practices, then, if you like, you can vary pot
or temperature or whatever to get shadings you prefer. Your cochineal can be
paired with various nuts or lichens to provide variety as well. Can be simple,
can be a long-term study. Fits well with what I've observed of the way your mind seems to work, but only you can gauge your interest.