Stop the presses.  I found a work-around.

Additional information:  If I specify a value for EditorWysiwygModeCss in the HTML tag, the Class menu is built from it, and if in addition, I specify a different file for EditorWysiwygModeCss in the Page_Load code, that is the style sheet that is used for the display. 

 

This suggests the idea that the drop-down menu is build before the Page_Load code is executed.  Perhaps the solution for me is to specify EditorWysiwygModeCss in an even that occurs before Page_Load...

 

IT WORKS.  You might want to either fix this or document it, but my application works as expected if I put the editor setting in the Page_Init handler, which runs before Page_Load.

 
        Sub Page_Init

            Editor1.EditorWysiwygModeCss = "rjSite.css"

        End Sub