Solution: First, make Windows 8.1's File Explorer show you the Libraries: On the desktop, in File Explorer, click on the View tab; under the Navigation pane icon, check the item marked Show Libraries.
Second, put the buried Public folder back in File Explorer's Favorites list: In File Explorer, navigate to C:\Users, then click and drag the Public folder to the top of the left side, dropping it in the Favorites list.
Finally, rebuild your Libraries the way you want them. Navigate to a folder Microsoft would like you to forget -- for example, \Public\Public Documents, right-click on the folder and choose "Include in Library, Documents." Repeat for Music, Pictures, and Videos, at least.