How can I tell which template a specific report instance is based on?
Short answer: with some difficulty.

If you only have access to the web interface, your best bet is to use the "Create Report from Templates" link under Reports to see a listing of all the available templates, and try the "Existing Reports" link on the most likely ones to see if the report is listed.

If you have database access, you can look up the report instance in the civicrm_report_instance table where it will tell you the class that the instance is based on, from which you can usually identify the report.

Providing the report template information on the report instance would be a great idea.