Why do you need to uncheck facing pages? You can export a normal PDF as single pages from a facing pages file.
This isn't a contact point for Adobe - this is a user to user forum where everyday users of InDesign help each other out with issues.
What you need to do is go to each page that has the image across spreads.
Copy the image.
Edit>Paste in Place
This duplicates the image over your current image.
Drag the handle back to the spine for one side.
And then select the image underneath and drag that handle to the spine.
This effectively puts the same image on each page, but they are broken over the spine.
When you untick your pages the images are retained in place.
If you have a lot of images consider asking on the scripting forum for a solution via a script.
@Eugene – hm, I would recommend something else, because "dragging the handle" wouldn't be sufficent for image containers that are rotated or images contained by free forms or containers with strokes…
Make a new doument with single sided pages and place the double sided InDesign document page by page on the pages of the singel sided one.
I'd recommend rotating the graphic within the frame rather than rotating the frame itself.