Googling this subject produced one hit: a bug report (more of a feature request) that dates from 2008. Considering the problems I'm having, I figure I'm overlooking something very obvious.
The only way I can see to edit a template is File->New from template.
If I change anything then save, it saves as a new document. So I have to Save as template, which means giving it a new name, new description, etc. Is this really the only way to do it?