Should I make a CMYK file with the image in the K channel only, leaving C, M and Y blank? If I place a grayscale image, will this result in a 4C black when I export to pdf?
No leave it as grayscale. Grayscales always export or print to the blackplate unchanged as long as the output destination is CMYK. If you put it on the black plate in Photoshop you might get the 4-color conversion you are trying to avoid (i.e., if you were to use a conflicting CMYK destination profile on Export or Print).
The CMYK profile itself is confirmed ISO Coated v2 (eci) 300%. If I place grayscale, is 15% dot gain the right one to use?
In Photoshop the gray profile adjusts the preview, not the output numbers, so if ISO Coated v2 (eci) 300% is the correct profile for CMYK it will also be the one to use for the gray profile. You can load it in PS via Color Settings>Working Space Gray>Load Gray... then choose ISO Coated
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I would make the grayscale conversion using the Black Ink channel from your CMYK profile. You can set that as the gray profile by making a custom color settings file in Photoshop and selecting the black ink under Grayscale.
You can save that directly fom Photoshop as PDF, or Tiff, or any other format your printer will accept. No need for ID at all unless youare adding something else. If you do need to use ID, assign teh ISO profile to the document, then place your grayscale image. As long as you don't convert to some other profile all of your black information will remain as black only and will be unaltered.
That's clear as day . Thank you very much both!
(Yes, Peter, I'm adding something, that's why I need ID).