Hi Harlan,
Just to be sure - I believe that:
-- 'Tools | Options | Engines | Name Mapping | Map object names automatically' was unchecked; and
-- 'Tools | Options | Engines | Recording | Do not generate variables' was checked.
Also, as you REMOVED namemapping from the project, you may try to navigate to the project root in the Windows Explorer and rename NameMapping folder to some other name. (This is just my wild guess that TestComplete may check if such folder and a file in it exists and suggest you to use it.)
