There were a couple of concepts I needed to understand first:
PhpStorm offers its own shelve/unshelve functionality, independent of any Version Control System
My files could not be found because "Main menu >> VCS >> Shelve changes..." put them in the IDE's shelf, not Perforce's. The IDE's shelf is inside <project-root>/.idea/shelf
What gets shelved is a set of changes since the last commit, not the file itself
This led to a fundamental misunderstanding on my part. I thought my files were missing because I couldn't see them in the OS folders, but what was missing were changes made to those files. It's because the files were new -- and thus the changes were comprised of the whole files -- that it appeared as though the files themselves were missing.
What actually happened when I shelved: the files were rolled back to their previously committed state (in my case nonexistent), and the changes were saved on the shelf
All shelving/unshelving is accessible from the Version Control tool window
Pressing Alt + 9
brings up this tool window. When items have been shelved, there is a Shelf
tab. From there, I was able to see the changes, and unshelf them. Thus I got my files back!
Perforce Shelf is accessible as a separate menu item
Open the Version Control tool window and select the "Local Changes" tab. one context option visible upon right-clicking a changed file within that tab is "Shelve changes...". This is equivalent to what I did originally and it will put the file changes in the IDE's shelf. When Perforce is integrated into the IDE project, the option I actually wanted appears as: "Shelve in Perforce..."
This option will place the files changes in the Perforce shelf (on the Perforce server) and rollback the working directory to the last commit state. The changes are not be visible within the "Shelf" tab of the Version Control tool (as this tab only shows the IDE shelf). To browse the Perforce shelf, go to the "Local Changes" tab of the tool, right click the appropriate Perforce changelist -- looks like <LIST-NAME> - Perforce #<LIST-NUMBER>; x shelved changes
-- and select "Browse Perforce shelf..."