I've tried to shrink the font . . .
How are you adjusting the font size? Is the text still editable? Or has the text been rasterized and you're just adjusting the rasterized text image?
If the text on the spine is still editable and not rasterized, try rasterizing it and see if that makes a difference. That is, make sure the text is no longer in an editable font but that it's been turned into a vector or bitmap or whatever format the cover is in. Flatten it, merge layers, whatever. Just make sure the text is no longer editable. Then see if it accepts it.
If Amazon's system is able to detect text, even rasterized, then that won't work. But, if Amazon's system is only able to recognize editable text, then rasterizing the text may work.