I believe that you can streamline this workflow considerably by working exclusively in iBooks Author. Simply use a combination of *.epub and *.ibooks templates in iBA and select/copy/paste the content from the PDF to each template. Adjust each version to take advantage of the format and export. Amazon will accept the ePub version as input to its publishing system.
The simplest ePub scenario will be text and static images only. I'd suggest using the ePub validator before rummaging around with Sigil or BBEdit. Note that this ePub will be version 3 but backwards compatible with version 2 of the ePub standard. Not only will these files convert well into Amazon's proprietary format but they will also be readable in other ePub 3 compliant eReaders such as Radium which requires the Chrome web browser.
Support for the ePub 3 standard varies from eReader to eReader. The Book Industry Study Group (BISG) maintains an on-line support grid that attempts to describe the degree to which eReaders comply with the standard's required and optional capabilities. There is even a test suite of ePub files with which to evaluate eReading systems. Apple's iBook app does quite well with the ePub 3 standard and, of course, with Apple's own proprietary *.ibooks format.
Thus, you may want to create additional versions of the ePub document that will read well in the iBooks app but not so well or at all in other ePub 3 reading systems.
The *.ibooks version of your book is limited only by your imagination and the extensive capabilities of iBooks Author.