I don't think you are changing colorspaces correctly. I think that only works if you start from RGB and go to some other colorspace. I don't think IM knows that your image is CMYK and so you need to tell it in a round about way. See
http://www.imagemagick.org/Usage/channe ... bine_other
where you will find something like this:
convert image_cmyk.gif -colorspace CMYK -separate image_cmyk_%d.gif
convert image_cmyk_0.gif -colorspace CMYK \
image_cmyk_0.gif -compose CopyCyan -composite \
image_cmyk_1.gif -compose CopyMagenta -composite \
image_cmyk_2.gif -compose CopyYellow -composite \
image_cmyk_3.gif -compose CopyBlack -composite \
-colorspace RGB image_rgb.jpg
I am not sure that this is causing your diagonal banding issue though! It may be that you are starting with a PDF file and that may be the issue.