Solved.
I noticed when editing the CUE file in notepad there is a status bar at the bottom of the window. I opened the CUE files in question and noticed the status bar at the bottom of the window (showing the cursor position, magnification, etc.) indicated "Unix (LF)" or "Macintosh (CR)" instead on "Windows (CRLF)".
I copied and pasted the text of the CUE file into an RTF document which I opened in Word. I was then able to search for consistent keywords (TITLE, PERFORMER, INDEX, etc.) as well as unbalanced double quotes ("), proper FILE name, etc. I then saved the document as a text file using the defaults in the "Save As" dialog.
I renamed the text file with a CUE extension making sure the filename was the same as the MP3 file.
Drag and drop the new file to the Music Bee "Playing Tracks" window and it works! View>Refresh in Music Bee will show the tracks in the main widow.