I'd like you to describe this "subjective immortality" experience a bit more, or at least how you imagine it. Is it just like, I die, and then my point of view shifts to another "me", elsewhere in the universe?

If I've understood your thought experiment correctly, then I'm convinced you haven't preserved continuity of consciousness — in fact, it has been explicitly interrupted. As a counter-example, imagine creating a perfect clone of yourself. Your subjective experience won't suddenly be you looking through two sets of eyes; you'll have your consciousness, and the clone will have theirs. If you choose to kill yourself, you won't suddenly "take over" the clone's consciousness; it'll keep having its consciousness, while your brain will have permanently (?) stopped being conscious. CGP Grey has a nice video on the "Star Trek teleporter problem" where he goes over pretty much this exact topic, particularly as it relates to the Ship of Theseus problem.

In my understanding, the key missing factor is hiding in your second paragraph — the continuous sense of identity relates to that arrangement of atoms, as it persists continuously through time.