How do I get iTunes to take my security update info?
Eventually, I gave the same answers but left the backup email blank. That was accepted by iTunes and I was able to finish up and continue downloading new apps.

Next, I went to https://appleid.apple.com and chose "Password and Security" where I entered answers to 2 of the 3 questions I just generated. Then I was able to update all the 3 answers and add a "Rescue Email Address".

I'm not 100% sure if omitting the email was what got it to work or if it was just a matter of timing but I wanted to post this in case it helps anyone else get past the issue.