Not the battery but the starter
Just to keep this thread up to date, I thought I'd let everyone know that the problem is apparently the starter, not the battery. After my complaining bitterly to the dealer about their quality of service, they suggested having the service rep drive my car as if it were her own for a few days. She did that, following the pattern that I had documented the last time the car had died, of three short trips after one relatively long one. The car died on her, so lo and behold, it wasn't just me! When I asked how she "diagnosed" the problem, she told me the dashboard lit up and the car went click, click, click. You'll note that was what I started this thread describing. I had also sent a video of exactly that the last time the car died.
To be fair, I had originally thought the problem might be related to the convertible roof as it happened most often it seemed when I used either the sunroof or the convertible top. And that was apparently a rabbit hole the dealer went down.
I am frustrated, however, because it seems as though they didn't ask me the right diagnostic questions. Maybe there's not an easy way to do that, but it seems that my saying the car "just went click, click, click" when I tried to start it, didn't register as the same thing as when the service rep experienced it.
Anyway, they are replacing the starter, but keeping the car for a few more days to test-drive and ensure this is really the solution to the problem. I'll post again once I have a final resolution, i.e., I have my car back and it doesn't die on me in the near future.