Forgot to mention on my previous post that this time I kept hitting "try again" in response to the passcode message. Each time I did that, the time left kept counting down. Finally after about 20 or more times, the time got to zero, so it thought it was done with the update.
Prior to that, when I got the error message, I just hit "cancel" and it thought the update wasn't finished. So, when I went through the process again, it tried to do the update from the start and I would get the passcode error message again.
This time, when I put it into recovery mode and reconnected to iTunes, it let me restore without asking me for the passcode first! I didn't do anything different in the process that I had done the last three times.
I think it's fixed. I really appreciate the help.