I got a phone call from USCIS. Yes, there is a real human being behind the website and chaos!
It would seem that the problem is sorted. We are told that an I171 is in Ethiopia with the proper age range. It will expire 3 days after we're due to travel home, but they are working on getting an extension there. For now, we'll travel on the one already there and this will give a week and a half to allow the new extension to get there a bit more slowly.
Yeah!!!!!!!!!! Thanks for praying! I'm off to finish those travel plans. Rosie, here I come.