According to a service rep I exchanged e-mail with, the Firmware for the mirror was issued specifically with 17.4.12. My car has 17.7.2.
I think the service rep was confused because they said that just because it was in 17.4.12 does not mean that it was part of the later release 17.7.2, and my car never got 17.4.2 specifically. I think there is no way that it's true; in order to reach all the cars, they would have included the firmware in 17.4.12 and later. Maybe they can remove it from updates in the future, once all the cars have gotten it, but tracking that is not likely worth the effort for such a small part of each release, and there is no way it has already happened. Easiest way is to remove it from updates once all cars are on 17.4.12 or later.
In any case, the service center said that my car has the appropriate firmware for the mirror, so I'll be taking it in to have it mechanically fixed. Rather than attempting a fix myself, I want Tesla to do it, so that they can learn from the error and apply the lessons they've already learned to my car. They will want to figure out how to fix it once and for all. I don't expect silicone spray on its own is a lasting solution, it tends to wear out in other applications.