I went back and deleted all the Time and DS1307RTC files I downloaded, just to be sure there are no duplicates. I re-downloaded them and re-imported them into the library, just to be sure everything is in the right place.
To import them, I did Sketch>Import Library...>Add Library. I then selected the zips from My Downloads. Now both the Time and DS1307RTC libraries appear when I go to Sketch>Import Library... and they are at the bottom under "Contributed." Unfortunately, I'm still getting the same error.
When I go into my Arduino Libraries and then into the Time Library, it contains three folders: Time, TimeAlarms, and DS1307RTC. Should I not download the separate DS1307RTC zip? Could that be my problem? I think the only difference is that the separate DS1307RTC Library has examples.