Procedure:
0. Download the appropriate Restore image for your iPad from Apple.
1. Finder>Preferences>Sidebar
2. Uncheck "CDs, DVDs, and iPods"
3. Recheck "CDs, DVDs, and iPods"
4. Disconnect your iPad, if already connected.
5. Connect your iPad to your Mac.
6. Hopefully, your iPad now shows up in Finder.
7. Wait for your iPad to be backed up (if it hasn't already been).
8. Option-click the Update (possibly Check for Update) button.
9. Select the Restore image downloaded in step 0.
10. Wait, prayerfully, while the Finder does its thing.
11. If requested, enter the iPad passcode.