Searching through other posts, I round reference to the /Cleanreminders command-line switch.  I tried it, first by temporarily editing my shortcut, and then directly in the command line "Run" window... "C:\Program Files\Microsoft Office\Office10\Outlook.exe." /Cleanreminders.   I have returned my shortcut to its original state, which uses the /Recycle switch.

Now when Outlook starts, I get a balloon over Outlook's icon in the system tray that reads as follows.  "Cannot start the reminder service.  Unable to show reminders."