Well here's the update: My car just got a new battery pack! They're telling me it's a brand new one, not refurbished, so hopefully it will add many years to the life of my car. There was indeed a problem with the original battery that necessitated a replacement, and although the symptoms were obvious, the car's computer failed to detect it. It got so bad that it actually died at Tejon Ranch on the way to the service center with 40% charge - due to a major cell imbalance it refused to charge so it had to be towed the rest of the way to Burbank. Since this was a defect covered under the 8-year battery warranty, there was no charge for the tow or for the battery replacement, and in the meantime I got another Model S as a loaner. On Monday morning I'll make the long trip down there to pick up the car. Looking forward to see how it turned out!
Hopefully Tesla takes a chance to analyze the data from your faulty battery pack and updates the automated diagnostics so someone else doesn't have to go through the same thing that you did.