Could print this with Discharge Underbase (or plastisol), 4 main colors, and then a transparent black (.2% black and rest shape) with matte additive going over the main colors to achieve a darker tone. You'll have to experiment with the transparent to get it to where you like it.
In the lower left bar, use the first green, top of the W is the second green, and bottom right bar would be the yellow, with the transparent black for shading you would get an awesome look, bright colors, and not have to mess around with halftones making an ugly looking "representation"
Works with water base discharge too with a better effect in my opinion, however your results won't be the exact same on screen with either, but a great screen printed version without halftones.