Can you try open a new CMYK document, select all from the original and Paste in Place in the new document. Try saving as a new PDF and see if that works. Sometimes when you change a Document Color Mode it doesn't work as you expect. Yes, it was designed it in CMYK mode and not converted.

You might need to go a little back and forth between the RGB and CMYK view in the color panel (don't change the document color mode yet). When you get the color, rasterize in the resolution you need. Then use the same color management setup in Photoshop and convert into profile.

Actually preserving the colour on the printer -may-be possible. So long as. (1) the printer is set up to use 6- or 7-colour process, which depends on the hardware - depends on what was paid for. (2) the file absolutely is left as RGB, CMYK must be forbidden in this case. (Tagged RGB should probably be mandatory). ^{For this project, use RGB. If your images are already cmyk, see if you can find original RGB files, if they exist, and use those. RGB jpegs will be slightly smaller than CMYK, and starting with RGB will likely give you better color than converting to RGB from CMYK (save for web or convert to profile in Photoshop).} . 294 368 396 85 417 4 388 328

convert rgb to cmyk illustrator without losing color