I don't have anything definitive to add yet, but here's what we know so far.
The Chinese gov't has said they can expedite our visas so we'll have them by Friday. Based on that, we made reservations to fly out of here on Sunday - one week from today. The flight is packed, but it looks as though we'll be able to sit near one another. And the dog is also cleared to fly. We lost our business class upgrade, however, and that's pretty disappointing.
So - assuming the visas are indeed ready on Friday, we'll be Beijing-bound in just one week. If not - well, we'll start this crazy dance all over again until we get it right, I suppose...