I think a mockup would provide a lot more clarity. I am trying to imagine how these pieces will all come together, so let me give it a shot...
The saturation is not really a problem, but maybe you will want to consider looking at your full value scale of all the colors. If it's not large enough, it could result in some of the tiles feeling more muddy than you'd like. Before really micromanaging your colors here, maybe you would like to try moving sliders around on hue, saturation, and possibly even brightness. This will quickly give you a range of different angles to look at your work in a fresh new way.
Other than that, maybe the only thing I could add is that you could try and build something with what you have now. If the base tiles don't feel good, then adding additional props likely won't improve upon the situation!!