I focused on the groups you mentioned and tried to make each group visible in grayscale. If the symbols have kind of the opposite meaning, inverting the colors would be an option (Pineapple's approach, more exaggerated):
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What you noticed is called
Hue shifting, which makes color ramps interesting. In pixel art, leaves on a tree are often colored with a green main tone, but the highlights tend to shift towards yellow and the shadows towards blue (because of the sun and blue sky). If you would just add white and black, the color ramp will look dull.
The colors i picked are far from perfect, in fact i'm not good at it so
don't take the following hints literally!. I was lazy and used the same hue for the highlights as for the midtones, i just added brightness and desaturated the color (move up and to the left in the HSB color model). For the shadows i moved in the opposite direction, less bright and more saturated (move down and to the right), additionally i shifted the hue slider, on the right, towards blue.
This is not a general rule! I just picked what looked interesting and did not balance all colors (for cyan i simply forgot to manipulate the hue, for others i shifted too much).
TL;DR google "hue shifting".