I do a lot of RGB to CYMK conversions at the toy company I work for. Since they are toys (educational toys actually) there are many bright colors. There are many times colors (bright greens/red) lose all detail during the conversion.
When I start this job years ago, it was still transparencies and scanning - Now it's all digital.
You do not want to take the saturation down before converting, that is compressing the gamut range of the image prior to conversion.
Edit>> Color Settings >> Settings: US Prepress Defaults (this will chaneg your other settings, especially good to have Adobe 1998 for RGB.
Then convert RGB to CMYK If you still need more saturation and detail.
Float a copy of the layer.
Change top layer blending mode to Soft Light
Change transparency to between 30%-60%
If image is slightly to dark do a curves correction and take the 50% midtone dot for all channels to about 42%.
The problem of going from RGB to CMYK you lose saturation, by your post are you experiencing the inverse????