This evening I kicked up the chroma with a couple more layers of red. Next came many layers of Viridian that simply did not give intended results--this pigment doesn't have much covering power. Switching over to Phthalo Green Blue Shade aggressively pulled the red into neutral tones. I don't know that I'd always want to shadow so heavily but I have learned an effective technique.
Now I need to spend some time composing a final image, getting the lighting just so.