In iTunes, I option-clicked the Restore button and selected a ipsw file of iOS5 that I had downloaded (iPad2,2_5.0_9A334_Restore.ipsw). The install then began, but eventually gave me this error: The iPad "iPad" could not be restored. This device isn't eligible for the requested build.
Thanks so much for any help you or others can offer! As I mentioned, by iPad now goes right into recovery mode when I start it; I can't see how to get out of recovery mode, so it's basically unusable.