I tentatively agree with all the points you make above. This is a general principle: it shouldn't matter where or when the mind making a decision is, the decision should come out the same, given the same evidence. In the case of instrumental rationality, it results in the timeless decision theory (at least of my variety), where the mind by its own choice makes the same decision that its past instance would've precommited to make. In the case of prisoner's dilemma, the same applies to the conclusions made by the players running in parallel (as a special case). And in the cases of anthropic hazard, the same conclusions should be made by the target of the paradoxes and by the other agents.
The genuine problems begin when the mind gets directly copied or otherwise modified in such a way that the representation of evidence gets corrupted, becoming incorrect for the target environment. Another source of genuine problems comes from indexical uncertainty, such as in the Sleeping Beauty problem, the case I didn't carefully think about yet. Which just might invalidate the whole of the above position about anthropics.
In passing, I said:
And lo, CronoDAS said:
To which I replied:
There's a certain resemblance here - though not an actual analogy - to the strange position your friend ends up in, after you test the Quantum Theory of Immortality.
For those unfamiliar with QTI, it's a simple simultaneous test of many-worlds plus a particular interpretation of anthropic observer-selection effects: You put a gun to your head and wire up the trigger to a quantum coinflipper. After flipping a million coins, if the gun still hasn't gone off, you can be pretty sure of the simultaneous truth of MWI+QTI.
But what is your watching friend supposed to think? Though his predicament is perfectly predictable to you - that is, you expected before starting the experiment to see his confusion - from his perspective it is just a pure 100% unexplained miracle. What you have reason to believe and what he has reason to believe would now seem separated by an uncrossable gap, which no amount of explanation can bridge. This is the main plausible exception I know to Aumann's Agreement Theorem.
Pity those poor folk who actually win the lottery! If the hypothesis "this world is a holodeck" is normatively assigned a calibrated confidence well above 10-8, the lottery winner now has incommunicable good reason to believe they are in a holodeck. (I.e. to believe that the universe is such that most conscious observers observe ridiculously improbable positive events.)
It's a sad situation to be in - but don't worry: it will always happen to someone else, not you.