And as for how the copyable entities will reason about their own existence
I'm not interested so much in how they will reason, but in how they should reason.
The sort of thing that might eventually give us insight into whether we're copyable or not would be understanding the effect of microscopic noise on the sodium-ion channels, whether the noise can be grounded in PMDs, etc.
When you say "we" here, do you literally mean "we" or do you mean "biological humans"? Because I can see how understanding the effect of microscopic noise on the sodium-ion channels might give us insight into whether biological humans are copyable, but it doesn't seem to tell us whether we are biological humans or for example digital simulations (and therefore whether your proposed solution to the philosophical puzzles is of any relevance to us). I thought you were proposing that if your theory is correct then we would eventually be able to determine that by introspection, since you said copyable minds might have no subjective experience or a different kind of subjective experience.
(1) Well, that's the funny thing about "should": if copyable entities have a definite goal (e.g., making as many additional copies as possible, taking over the world...), then we simply need to ask what form of reasoning will best help them achieve the goal. If, on the other hand, the question is, "how should a copy reason, so as to accord with its own subjective experience? e.g., all else equal, will it be twice as likely to 'find itself' in a possible world with twice as many copies?" -- then we need some account of the subjective e...
Scott Aaronson has a new 85 page essay up, titled "The Ghost in the Quantum Turing Machine". (Abstract here.) In Section 2.11 (Singulatarianism) he explicitly mentions Eliezer as an influence. But that's just a starting point, and he then moves in a direction that's very far from any kind of LW consensus. Among other things, he suggests that a crucial qualitative difference between a person and a digital upload is that the laws of physics prohibit making perfect copies of a person. Personally, I find the arguments completely unconvincing, but Aaronson is always thought-provoking and fun to read, and this is a good excuse to read about things like (I quote the abstract) "the No-Cloning Theorem, the measurement problem, decoherence, chaos, the arrow of time, the holographic principle, Newcomb's paradox, Boltzmann brains, algorithmic information theory, and the Common Prior Assumption". This is not just a shopping list of buzzwords, these are all important components of the author's main argument. It unfortunately still seems weak to me, but the time spent reading it is not wasted at all.