Here are my latest results. I promise to drop the whole thing now. But I am by no means satisfied, and I'm wondering if those of you with more experience with dyeing might have some insight into this.
The cloth with the splotches was my experiment, mixing up various proportions of boysenberry and turquoise and applying it to white cotton with a paintbrush. The ratio I settled on, the column of splotches in the centre of the photo, was 1 part boysenberry to 3 parts turquoise. You can see how the turquoise migrated away from the boysenberry.