How to limit the ink coverage in Illustrator?

Im working on a playing cards set for a client. The background of the cards is a pretty dark bitmap image.

I don't usually do a lot of print production however this time there was no way around it. This is the reason why I might not see the obvious, if so I'm really sorry.

Anyways, the printer demands a maximum ink coverage of 300% and specifies the color profile as Coated FORGA39 (ISO 12647-2:2004).

When I export the PDF the color coverage is above 300% in vast parts of the image, which I did expect since Illustrator does not change the colors of bitmap images as I understand it.

That's why I opened up the image in photoshop and set the color profile there as well. The Info Window says that the ink coverage is below 300% in the critical parts, but as soon as I export the picture as a PNG or PDF the color coverage is above 300% again. The same thing happens if I use another or a custom profile with a coverage less than 300%. If I export as a JPG and untick the ICC Profile the image gets exported with all of the coverage below 300%, this however is no solution since I have to insert a lot of PNG pictures with a transparent background.

Now I have 2 questions:
1. How do I export my PDF correctly with all the color coverage below 300%?
2. If I have to edit the color for all bitmaps (over 40 files) manually in photoshop, is there any way to d this for multiple files at once?

Thanks in advance, any help is appreciated since I really don't have any idea what to do anymore.