Ah! so you're defining "this" as exact bitwise match, I see. Certainly that helps make the conclusions more rigorous. I will suggest the way to handle the after-the-fact coin flip bet is to make the natural extension to sufficiently similar computations.

Note that even selfish agents must do this in order to care about themselves five minutes in the future.

To further motivate the extension, consider the variant of Newcomb where just before making your choice, you are given a piece of paper with a large number written on it; the number has been chosen to be prime or composite depending on whether the money is in the opaque box.