We found something that worked for us (thanks to Canvas Support).  It turns out we needed to delete the "section" under Course Sections in the course Settings/Sections page before it let us click on the option to "Enable course as a Course Template".

It would be nice if this were mentioned in the Canvas Guides somewhere. They just say "If you are unable to manage the Course Template setting, the course may have enrollments...".  Perhaps by "enrollments" they mean "sections".  😉

Hope this helps others.