After I deleted the offending CPH from the template, the Content Block that I had originally placed there seemed to be rendered in the first CPH it could find. It stayed put after I moved it to another location and published the page.
It also seemed that, when the editor loads, none of the buttons or links in the page editor worked as expected if a widget is displayed in that CPH. I had to use my "Back" button to get back to the admin section.
The process seems to be:
1.) Remove the place holder found in the Head section of your template.
2.) Edit the page and drag the widget from wherever it rendered to the desired place holder
3.) Re-publish the page
I submitted this information on PITS but it isn't displayed for voting yet.