Well -- I did some further research and discovered this post
https://www.mobileread.com/forums/sho...d.php?t=141722
The important thing I found in that post was that *.MOBI files can be renamed *.PRC and the Kindle Fire device should be able to read it.
Sooooooooooo -- I tested it.
I went into my Kindle folder and renamed a book title sent over from Calibre from .MOBI to .PRC
The device now recognizes that the book is in the Main memory where it ignored it before. I can read the book and the cover shows up, etc.
I don't know if this information is going to be of any use to anyone else -- but I thought I'd share what I'd discovered.
I'm still going to delete books from the Kindle as Kovid recommends and add them back and see if there's a "problem child" causing all this mayhem.
But at least I found a workaround in the meantime.