Well, this is embarrassing. Turns out my wife didn't read through her info packet after getting the car and neglected to send in the signed DMV forms. This is her car (solely in her name), so I'll do my best to blame her. It's our third Tesla, but it was the first to be dropped off without us being present during "delivery". The first car they dropped off while we were home and we signed everything then. The second car we picked up at the delivery center and signed there.
I suppose it's my fault for not double-checking what she was supposed to do. I owe both Tesla and the DMV an apology for disparaging their good names (despite the fact that the DMV couldn't have possible been less helpful).
We dropped off the paperwork at the factory showroom this evening and the seemingly-knowledgeable woman there said they'd expedite the plates through the DMV and to expect them in a week or so. BTW - On our way out of the factory, we went south on the little frontage road past the staging/transport lot and it was absolutely full of cars being loaded onto trucks. This was around 7pm