Yeah, the total lack of any coastline visible during the battle makes the whole thing crazy. Even if Yokohama proper subsided that far (which would cause a ludicrously huge tsunami), you should still see the rest of the new coastline somewhere in the background of at least one shot.
As it is, I think you're right that the writers just used Yokohama for the pure cool of it, like an American writer would put in some recognizable landmarks like the Hollywood Sign or something in a disaster movie, never mind if it's location or depth would make sense.
1000 words of update done so far. On track to post by Friday.
Maybe it was an artificial island that got swamped and sank by the tsunami generated by Second Impact?