As alluded to, we'll have to wait a little longer. Tesla would not do a warranty replacement while Mobile Service was out. Tesla recommended I disconnect 3rd party apps (I did already try this, but did not change the password, just logged out; however, I forgot I had ABRP connected still, so who knows what it was doing). So I've redone my password and we will see; only the Tesla app can connect now.
We'll see what happens. I actually think it's possible this could have been the issue - it just is hard to understand how this could be a battery issue with the way it is behaving. I guess I'd give it even odds.
Maybe next week I'll have resolution. I do think that I'll probably go pick up a Tesla battery even if it starts looking fine - just to have it ready to go. Relatively cheap insurance.
It doesn't appear there is any need to do any of the underseat disconnect procedure for a 12V battery replacement; the Mobile Service did not bother with that. Though he did have a battery charger as well, to give it a boost while he was working on software updates. In any case, it should be pretty easy to replace.