My new passport is here and after a couple of days running around town, making phone calls, and arguing with my wife, I was able to make it to Japanese immigration today with my library of documents and apply for my visa extension. We'll see how long it takes them to do this one. I'm just happy to have it off my mind for the weekend.
The people at immigration were actually not that bad. They seem to know what they're doing more than the people at the city office. The people at the city office are notoriously bad. So bad, in fact, that Yoko has had negative things to say about them. Perhaps bad is the wrong word. Incompetent is maybe better. They aren't rude or mean or anything.