Here is the latest on my situation.
Tesla have had my car for just over 2 weeks now. They ran diagnostics and have determined that there is indeed a "problem" with the high voltage battery. The good news is that all repairs will be done under the battery warranty (my standard warranty expired a couple of years ago). The bad news is that - they are going to fix the battery, rather than giving me a new one!
I don't have the details yet on what exactly the issue is, but this is how it will play out. They will swap out my battery for a loaner battery, and I can return the loaner car. They will then send my battery back to the factory for repair, at which point, they will swap it back.
I'm actually looking forward to getting my car back - For the last two weeks, I've had a taste for what it's going to be like in 2019 when the white carpool stickers will no longer allow access to the HOV lane.