Reading carefully all this info. I did a "Walking in a Winter Wonderland" in blues. Used transferease so after done embroidering had to soak each 'square' to get that off. Well the blue did bleed. tried many different things. put it away for many months. then I soaked it (I had already sewed it together) in oxy clean a couple of times. It did a pretty good job of cleaning up the mess! Some of the blue embroidery thread was old which perhaps made a difference but when using it in dishtowels it was fine.
I will try this recipe in reds and blacks especially.