And, if this is more your thing, here:
Of course, there's a twin of this color layout (swap vertical pairs of dots with horizontal pairs). I haven't tried the twin yet, but this layout is much nicer than the crazy thing I was working with earlier in the evening. All of the dots are the same distance from their nearest neighbor (but a little ring of 5 dots isn't a regular pentagon - that's going to have to be OK).
There's still 5 different colors under the vague category of "green", and 3 distinct "pink" colors, but I think I can work with this.