Hello Armin,
I will work my way through your essay! Thank you for reading mine in detail. You are right to notice that I did not really advocate a particular interpretation of QM. (I also didn't advocate strongly for discrete vs. continuous: anywhere between the discrete skeleton of the Ultimate T-shirt and the fully discrete digital physics would seem possible--including continuous but countable, allowing only rational numbers, which could be expressed by networks of unlimited but finite size).
For QM interpretations, (1) I find Many Worlds with decoherence to be promising, but I know critics have problems with the "preferred basis problem" and some doubt whether the Born probability rule is really proven. I haven't looked into these criticisms in enough detail to see if they are merited. I don't think the criticism from Occam's razor is justified.
(2) This is something I tried to do in the Appendix, though ran into time constraints: try to take the projection that occurs in measurement as fundamental and work backwards to what physically that would imply, in other words, some form of Objective State Reduction.
(3) In fact (1) and (2) don't have to be so different. It could be that Many Worlds works, but we might be able to describe our own superposition as if it were the only one (my essay gives the analogy of describing a surface as curved without having to describe an embedding space: similarly we can describe the random projections without describing a ghostly superposition we'll never measure.)
A paragraph got edited away, but I'd originally emphasized the danger of trying to draw broad philosophical conclusions from QM, which grew piecemeal and empirically, and still might be an Early Quantum Theory. I don't think there's much "going back" to pre-QM realism, but "It from Qbit" strikes me as summarizing empirical results more than fitting them into a coherent guide.
One could say pre-information is information that's isolated, as information only exists in relation. A reductionist approach to information stops at the Bit, but as a placeholder, a Bit alone does not convey information, and neither does a symbol in a formal system.
Another thing space constraints prevented me from elaborating on: obviously in a deductive system like Zermello-Frakel-with-Choice, there are other axioms besides the Axiom Schema. And in the Ultimate T-shirt view of physics, the axioms are chosen very carefully. What I wanted to emphasize is this particular structure, the deductive system, and its versatility, and its presence in the standard view of what physics is trying to do. And beyond that, the "magic" needed to make mathematics *go*, is not needed in many cases, such as for axiom schema.
I was arguing for the general reinterprability of formal symbols as the means by which information can take different forms--a branching tree, generally a semi-Thue system or term-rewriting system (viewable as a graph through L-systems).