Thank you, that's very helpful!
Yes, the police report is the main blocker. (I am a US citizen and a legal resident of Germany.) I have an appointment for Jan 28th but, it being Berlin, that doesn't guarantee that anything will actually happen that day. As a dirty foreigner I'm not allowed to do it online. The other potential delay is getting an appointment at the Embassy, but from what wprime says it sounds like that will be OK if I ask for an appointment once everything is ready. In Berlin they don't process anything by mail; in Los Angeles they *only* process things by mail.