N0m: You’re going out on a huge limb to avoid acknowledging that the Halacha is a practical one that’s in effect in the normal course of life. I dare speculate that the reason you’re going so far out of your way to avoid acknowledging the practical effects of this mitzvah is a result of being ashamed of it when having to explain and justify it to non-Jews and secular Jews who, with their 20th/21st century Western mindset cannot conceive of such a law set by G-d.
It’s the same thing other people do regarding kaparos, mezitza b’peh and even plain ‘ole Bris Milah itself, among other “archaic” Mitzvos and obligations.
The facts of the matter are that on the Titanic you had masses of people congregating on the deck angling and pushing to get in to the limited number of lifeboats. They were all there together, many masses of people, that the crew had to select from right in front of their noses. As such, this is certainly a very clear case of were this Halacha we’re discussing in the Mishna and Shulchan Aruch would certainly apply.