For anyone following my story, they called me *12 minutes* before my appointment to tell me they have additional things and wanted to postpone delivery. I asked whether I could see the issues, but didn't get an update from them for a while, so I went into the SC to speak to someone in person. They were fine with me taking delivery and noting the issues to be fixed, and honestly it wasn't anything big. Biggest issue that they found themselves was one scratch on the front left fender that they'll have to sand and repaint, and the front two fender trim pieces will need to be replaced because they aren't seated correctly.
I think I probably found more issues myself (typical Y stuff, back seats, slightly misaligned hatch and consequently a small corner of a taillight is roughed up a bit on the edge, couple paint nicks, etc.). Nothing seemed like it couldn't be fixed or would be dangerous to take a gamble on, so I took delivery and just have these things noted for repair.
Overall, I'm not particularly happy with the lack of communication, but very happy with the car itself. All part of the Tesla experience.