I don't think it's about the greys being subdued enough I think you just need to be a little bit more selective on what you want to color. Where do you really want to draw the eye?
Currently you have reds all over the image which will draw the eye all over the place if you are a little bit more restrained you will get a better effect. Less is more.
I have taken the liberty of editing your photo I hope you don't mind. Obviously, there are lots of choices you could make here on exactly what you want to color.
Best,
-Q