I was able to install the "Directory" plugin just fine. It created three pages for me, "Edit", Create", and "View" listings. Since I did not want three pages for the same thing on the home page, I moved them all to be under a single "Directory" page. I think this is where things went terribly wrong.
I had not tested the plug in before moving the pages, but after I moved them, I tried seeing if it worked. The Create Listing page wouldn't let me attach images to a post. Clicking that button just sent me to a white page. I could create a test listing that showed up on the lists of listings in the dashboard (not on the listing page though). But when I tried to view that listing through the dashboard, I got a 404 page not found error.
I tried to get it fixed while chatting with the help guy in the chat room, but we made no progress. If anything, it got worse. I deactivated the plugin and reactivated it. Deactivating it apparently caused those three pages to be deleted. Reactivating it did not bring them back. Similarly uninstalling and reinstalling the plugin did not bring them back, but obviously the settings had not been deleted when the plugin was not installed since my test listing was still there after the second installation.