Illustrator CS5-Multiply used on tiffs are now hazy-gray in CMYK?

Question

I have created AI documents in both RGB and CMYK document color modes. In both modes, I have a colored background or a photo. A TIFF file is Placed in the AI document on top of the background. It contains black line art on a white background (flattened in Photoshop, grayscale, Tiff). I use the Transparency>Multiply feature to drop out the white background, and leave the black portion of the artwork. I have other CMYK AI files with perfectly transparent artwork created yesterday. Everything is fine in RGB, all transparent...but the printer will need it in CMYK.
Today, I was working unbeknownst, in an RGB document, and in the middle of this project, changed the AI Color Mode to CMYK. Now 7 of the 10 Placed, Multiplied files have a gray "haze" over them that exists whereever the white is on the original file. Although I see these haze-gray boxes in the AI document, they come out transparent in a PDF file.
After doing that, I cannot create a new, fresh AI document and recreate the transparent backgrounds on the same Photoshop files in a brand new CMYK document using the identical placed tiffs.
In addition, the same files I used in the original document, are placed in the brand new document (For example, a dragonfly ink drawing.) The SAME tiff file now placed without any background AROUND the dragonfly but white windows in the wings where there aren't any black lines.When I Multiply, the area around the dragonfly is clear, but where the white was in the wings is now hazy-gray.
When I SAVE AS a PDF file, NONE of the placed tiffs are visible.
What have I done to change the way CMYK files are handled??? I was also working with drop shadows, and color swatch changes, on text, at the same time I decided to change the Document Color Mode.
Is there a better way to drop out the white background?
I use a iMac, OS 10.6.4, and Creative Suite 5.
Thank you in advance.

Answer 1

Thank you. I'm not sure I'm responding to the forum correctly. I can
only respond through the email, can't find the Forum instructions on
line, and can't upload an image.
I checked the image modes in Photoshop. The PS files are not bitmap,
they are all grayscale. I use grayscale because I sometimes have to
colorize the black and white line drawing to a color, that can't happen
with RGB or CMYK.
The printing method is a large inkjet-type print (not offset), a single
print, then high-pressure laminated to a product similar to Formica. The
printers have not had a problem with this method I've used before.
(there are no color separations).
These files are huge because of the line art. A file that is 24"x36" 
and 150 dpi preferred by the printer, makes the files very large. As I
understand it, a bitmap of ink line art needs to be 1200dpi, and at that
size it would be just huge.
In response to Doug's comment about how about combining all the "bitmap
work in PS and place the composite in AI as a single linked image".
Right now, with the client shifting the images around so, it's easier to
build the AI document with all the smaller vignettes as tiffs (which was
working up until this afternoon!). But I could consider combining it all
in PS, unless there was some layering issues. Like a giant puzzle piece.
I still don't understand why this is now happening to a new document.
And will it now mess up all my other projects that are half completed
and not corrupted. This has thrown me, entirely. I know just enough
about Illustrator to get me into a lot of trouble.
Many thanks!