It would be helpful to know how the image will eventually be used - I assume with the CMYK conversion that you are going to 4 color press...
Having said that, I suggest that you try adjusting saturation in Camera RAW. You can find this among the tabs on the right hand side of the dialog box, down below the histogram. Look under the tab that looks like a zig-zag - it is the fourth tab from the left. There is a tab under that called Saturation. Instead of three channels in RGB, or six in LAB, you have eight channels to work with.
You will also be working on a RAW image, which may give some advantage in reducing color distortion.
I also suggest that you consider sticking to RGB workflow for this, and convert to CMYK at the end of your editing cycle.
David