First things first, @Jay313, kudos for impeccable taste in Sci-Fi. Sadly, ol’ Blade Runner has suffered a little as being the ‘Shawshank Redemption’ of Sci-Fi (i.e. people lie about having watched it and/or having liked it).
That said, as an exploration of what it means to be ‘alive’, I think it is top-draw. I also think there is something almost Ecclesiastes-like about that the famous ‘tears in rain’ scene that the film builds towards. If we remove God from the picture, what does it mean to ‘live under the sun’? Are we all just machinery that will one day wear out? Are we just data on a hard drive that will one day fail to boot? What happens to all that data then? Lost forever…?
I really like this analogy, @Laura. In The Doctrine of God, John Frame talks about how God’s omniscience means that doesn’t just know all things quantitively, but knows it omni-perspectivally. That is, he knows everything from every ‘angle’ too or put it another way, God doesn’t just know all the data, he knows all the possible ways the data can be interpreted by individuals and groups throughout history too.
For example, imagine a pyramid and you and I are standing at opposite corners. You can see faces A and D and I can see faces B and C. But from our viewpoints neither of us can see everything. You can explain your perspective to me and vice versa, but neither of us can see all five sides at the same time. Even if everyone in the world gathered in a circle around the pyramid some information would be hidden (eg. the fifth face, the bottom) and some perspectives would be missing. For example, how the pyramid looks from above.
But God, John Frame might argue, doesn’t just know everything there is to factually know about the pyramid - the sum of all five sides if you like. But also knows it from all perspectives, he knows how you and I ‘view’ the sides, but also how the pyramid looks from all angle individually and at the same time. He also knows what it looks like when coloured by or freed from personal perspectives. He knows how it will be viewed by every living thing throughout time, including the fly buzzing around the third brick from the bottom.
How does this relate to the OP? Personally, I think the self is more than what I do, choose, and experience. But even if the self was only the sum of my memories, God is more than capable of reconstructing me with my true-self in the new creation. He can do this because he knows not only what I did and choose to do (because he knows all things), but also how I remembered, felt, and experienced those events (because he knows all perspectives too, including my own).
If John Frame is correct and if I have done a good job of explaining his position, then, perhaps, The Cloud is a great way of thinking about God in this instance. If that is the case, then moments are never lost like tears in rain because God knows both where the tears fell but is also able to reconstruct the tear to exactly as it was before it merged with the puddle.