The way I'm seeing it, that dropdown box you're selecting black or all in should not affect the appearance of the banner at all. It's in a section for labels and marks and should only affect the color of labels and marks. If you are truly changing only that setting and the print becomes oversaturated like the right hand result, there's something wrong with that RIP.
The settings you need to adjust for output are in Corel Draw's Color Management Settings for rendering intent.
When you export the pdf, make sure that on the export settings Color tab you have "Use Document Color Settings" checked and Output Color set to "Native".
DO NOT convert your photos to CMYK in the layout. Leave them as RGB, and these settings will let them be exported as RGB. The RIP will most accurately interpret them as it converts the layout in the ripping process.