But if you are literally talking about the same computation, that computation must be unable to know which instance it is operating from. Once the question of getting identified with "other" instances is raised, the computations are different, and can lead to different outcomes, if these outcomes nontrivially depend on the different contexts. How is this progress compared to the case of two identical copies in PD that know their actions to be necessarily identical, and thus choosing between (C,C) and (D,D)?

The interesting part is making the sense of dependence between different decision processes precise.