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If you want to keep the spherical 3D effect, then there needs to be dark and light shading that necessarily affects the "flat" base color. But if you follow my suggestion, everything will remain in the same Hue family and the colors will look more correct vs. the color swatches.

In that same gradient overlay layer style, the layer style itself has an opacity setting. Once you change it to Luminousity, you can also experiment with the opacity setting to get slightly altered 3D spherical effects.