I pulled (frogged) the offending white tones and have replaced them with the DMC 5200 bright white. I'm much happier with the effect.
I need to finish filling in the center of the flowerpot with white and four spaces with a pale gray. That's 1) kind of boring and 2) something I can do without needing the chart, so I've moved onto the flowers for the moment. This also has the benefit of being more interesting color-wise.