Make yourself intra-universally interesting enough that the alien construction management AI might instantiate a simulation of you from the cached info at some point. It's a strange sort of Darwinism, but it's all we've got.
(Of course, you could say that everyone's ceasing to exist, here, because your rules of what counts as a person and what's their copy applies to everyone. But please realize that, from the point of view of those who think having a copy survive is better than all of them dying, and is partial survival in some sense, that being simulated is a form of winning, even if you think both the person and the copy are deluding themselves.)
(Though I do wonder how you go about the day without having a nervous breakdown, given that your evolving state is probably quantized, or at least sliceable, meaning there's no great physical difference between your pattern shifting from one [smallfractionofa]second to the next, destroying the old one and replacing it with a new one, and your old pattern being destroyed and replaced somewhere else. It's not like your past self is aware of your future copy in normal life, either!)
(I'm not saying you're wrong; just that the situation is a lot worse than you think it is, and that we should all be living (and repeatedly dying) in absolute existential terror.)
Of course, one could argue that me having a past is a complete illusion anyway, as I am just some atoms.