Sorry for the self-reply but there is a second part here: Assuming there is no way to get around having these "answer bubble" graphics being stored redundantly in my document, what is the best way to make them as small as possible?
I am going to try SVG since the files are really simple (one circle and one text character). If that works, the files will be smaller by a factor of 1,000.
InDesign doesn't support SVG without a third party plugin.
The problem with the file size is not because of the image, but because of the preview, so I don't think file type makes any difference...
If the graphic is a simple vector, you can try pasting from Illustrator as native InDesign paths. Those don't have preview images.
Does InDesign still save one preview per instance if you only mount the image once and then make additional copies from the first instance?