Finally, it does really work.
BookFab Version 1.2.0.2
Kindle Desktop Version: 2.4.0 (70904)
I can now download and convert my Kindle books.
Quirken
Yes, the manual process of downloading the book using the Kindle app and then selecting and importing the local file in BookFab for conversion does work; however, the "eBook Platform Access" for AmazonKindle in BookFab is still not working. If you mouse over the option in BookFab, it pops up a message "Amazon kindle service is temporarily unavailable. We're working on a fix."
The manual process did allow me to download and successfully convert my "Complete Wheel of Time" (14,276 pages) which did not convert using version 1.2.0.0 or 1.2.0.1.