A certain icon overlay doesn't work in Windows

With thanks to Buster from Dropbox support, I resolved this problem.  In case anyone else has a similar issue, here are the steps that I took.

1.  Uninstalled Dropbox and restarted my computer. 

2.  Using the registry editor (Run REGEDIT), deleted "Dropbox" and "DropboxUpdate" registry entries, checking the following two locations:
HKEY_LOCAL_MACHINE\SOFTWARE\WOW6432Node\
HKEY_LOCAL_MACHINE\SOFTWARE\

3.  Made sure that remaining Dropbox folders did not exist or were deleted by checking the following locations in Windows Explorer: %APPDATA%
%PROGRAMFILES%
%PROGRAMFILES(x86)%

4.  Manually deleted any remaining Dropbox icon overlays in this area of the registry:  HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\CurrentVersion\Explorer\ShellIconOverlayIdentifiers

5.  Restarted my system and installed the newest version of Dropbox.

6.  After Dropbox installed and everything was indexed, I made sure that the ten Dropbox overlay icon overlays were in the first ten spots in the registry area from step #4. 

7.  I restarted my system again, and all the icons worked.  (I use OneDrive for work, and the icons there stayed in place even though their overlays are now "subordinated" to the Dropbox overlays in the registry.)

A complicated fix for a relatively minor problem, but glad to have the mystery solved.  Thanks again to Buster from Dropbox support!