I didn't know you could upload an .epub to KDP - and, presumably, let them convert it to .mobi. That sounds good.
I've created three .mobi files of the book: (1) by exporting to .epub from InDesign, then converting to .mobi (both) in Calibre; (2) by feeding the .epub into Kindle Previewer and letting Kindlegen create the .mobi; and (3) by exporting to Kindle using the ID Export to Kindle plug-in. The first looks fine in the Kindle Previewer and Kindle app: fonts are embedded (for Kindle Fire) and it has a nice-looking TOC. The second looks OK too, but lacks a TOC. And the third looks awful: no embedded fonts in Kindle Fire (not even Arial!) and a terrible-looking TOC.
I've received a less-than-helpful reply from KDP:
"When you upload the MOBI file generated using Calibre, we cannot guarantee that it'll successfully go through the conversion and publishing processes. Some files might not have any problem going through the conversion and publishing processes, but we cannot guarantee all the files will be successful. For this reason we request you to upload a MOBI file generated using Kindlegen, and republish the title."
If KDP has a problem with some Calibre-generated .mobi files, but not others, then I should think this is a issue which the developers of Calibre ought to address.