Jabba, since you can't stop trying to "essentially prove" immortality, and I am nothing if not helpful, here are my poorly worded suggestions:
(1) Drop the "soul" assumption. It is a multiplication of entities, is non-explanatory, and is just plain unlikely. Why does the particular soul that is "you" exist, out of an infinite set of "possible" souls? To "explain" that, you have to make even more unlikely assumptions. And the longer your list of unlikely assumptions gets, the less likely it is that they are all correct.
(2) Drop the "OOFlam" assumption that one particular body is the only "you" that can ever exist. This may require defining sentient experience in a way that will be unpopular in this venue. So be it. A man's gotta do what a man's gotta do.
(3) Stop letting your opponents derail you with the "Texas Sharpshooter" nonsense. You did not "cherry pick" a "you" from a group of yous. That "you" is the only one available. Nor is a hypothesis invalid simply because it is post ante, if the observation upon which the hypothesis is based is sufficiently compelling. My poker nemesis, whose style of play I know nothing about, just went all in on the river. It could be an all-in river bluff, but I'm leaning toward the hypothesis that he has my top pair beaten. That's a post ante hypothesis, based on a single data point. Is it invalid? A guy could learn a series of costly lessons about how reliable a post ante hypothesis based on a single data point can be.
Hint: the correct anthropic assumption is that what you are experiencing is typical, rather than anomalous.
Drop (1) and (2), and what you are left with is your best shot at making a case for any semblance of "immortality". Hold on to (1) and/or (2) and you've got no shot at all.
But "prove" it you will not.