Converting to Black and White from CMYK

I have a question regarding converting a color digital file to black and white. I like very much the technique of adding the two Hue/Saturation layers and then making adjustments to convert the image to black and white.

However the specific image i am working on is destined for the printing press and i have it in CMYK not in RGB. After adjustment with the two Hue/Saturation layers, the image becomes monochrome, but with a light red tint and it's not quite black and white. I went back and tried this technique on a RGB version of the file and it looks good.

Any suggestions? Can the two Hue/ Saturation Adjustment layer technique work correctly on a CMYK file or does it have to be applied to a RGB file? If it does not work optimally for a CMYK file can someone recommend another technique that would work well on CMYK files?

thank you, if someone could help me out here, i'd greatly appreciate it...

Honestly, just make it a lot easier on yourself and first convert the image to RGB, then apply the b/w conversion, then convert back to CMYK for printing. Yes, this could introduce image posterization, but if that is not a problem then this is probably the easiest and fastest method...