It turns out that the Nexus 7 definitely needs the Google USB Driver. Finding, downloading, and installing this driver worked perfectly.
Because Google's Android OEM drivers page does not include the Nexus 7 in its list of devices that need the Google USB driver, I had been trying the driver from Asus, which did not work. I did not try the Google USB driver because for some reason my SDK manager said it had downloaded the driver, but the driver was not to be found.
Finally I found I could download the Google USB driver from this page, which clarifies that all Google Nexus devices need this driver. Now I have successfully re-connected the tablet to ADB.
I submitted a documentation bug report to Google here in hopes that the OEM drivers page can be updated to reflect that all Google Nexus devices need the Google USB driver.