There are several options I can think of-- none of which will be quick & easy.
#1 If you can somehow convert your data into continuous measurements, you could put them on an XY plot. THEN you could use Add Reference Lines (bands) to color the different areas appropriately.This would be a hard-code fix: if your data changes around (or gets filtered by the user), the bands probably wouldn't fit.
#2 You could stick with colors TEXT rather than backgrounds
#3 You could make multiple views (3) and "stitch" them together in a single dashboard. Leverage the LEVEL colors to get the colors you like. If your users don't need to do any scrolling, this could work for you.
#4 You could wait. Tableau has said it's unveiling True Transparent Backgrounds (AT LAST!), meaning you could float your view on top of a color-banded view. But who can say when these will roll out.
I hope this is a little inspiration