Export RGB images/doc to CMYK pdf

[Meh12345678910]

Complete beginner here. I have a book with thousands of RGB images on a black background, some of which sit in black rectangles as extensions of that background. The first printer I used wanted an RGB PDF (presumably they do CMYK conversion later), so that was easy enough to export under the interactive/web option. 

However, the second printer wants a generic CMYK version. When I try to export (US Swop 2; convert to destination; preserve numbers), the black on the background of the images does not match the rectangles behind.

Tranparency blending is set to RGB. Black rectangles are RGB 0/0/0. Black backgrounds on images are also RGB 0/0/0. I've checked and double checked that. But in the CMYK PDF output, they are very subtly different. Is there a quick and easy way of rectifying this?

[rob day]

Thanks. I did actually try making a single page to share, but for some reason the file is still 149mb!

Try making a new InDesign document, open your layout and from the pages panel drag one of the problem pages onto the new document. Save the new doc and attach it here along with the linked image.

[Peter Spier]

If the blacks are the same in the PDF, but print differently on press, the problem could well be the RIP handling raster and vector content differently.