OK, I've had a little time to read now, so I can perhaps try to add my two cents. First of all, I think your realization that diffeomorphism invariance implies that a continuous manifold in GR doesn't contain more information than some triangulation is something that deserves being shouted from the rooftops---I've always thought that continua are something of an ontological burden, and should be avoided if possible. (The argument, or rather side remark, I make on this in my essay is essentially due to Achim Kempf---maybe you're familiar with his approach.)
I also was struck by the relationship you uncover between measurement and undecidability---this is another one of those ideas that keeps cropping up in unexpected places, and something I keep coming back to without, however, coming up with much of anything concrete (I've said a few things about this on the thread of Lawrence Crowell's essay). Perhaps the paper by Paterek et al., where they propose that outcomes of quantum experiments are random iff the proposition they encode is undecidable (from some set of axioms encoded in the preparation procedure), is of interest, but maybe it's a blind lead. Brukner has done some further work in this direction, and together with Zeilinger, has also professed views drawn very much from Weizsäcker.
Regarding Weizsäcker, yes, I think many of his cosmological arguments look somewhat quaint from a modern perspective, especially all the 'large numbers'-stuff, so I wouldn't want to commit myself to a 3-sphere cosmos as well. But I believe the argument for the 3-dimensionality of space being related to the 3-dimensionality of the qubit state space is not without merit; recently, it's been put into a modern information-theoretic form by Müller and Masanes. Of course, I suppose that to you, the advantage of 4-d spacetime is that it gives you a lot of smoothness structures to play with! (Incidentally, with your argumentation regarding 'the spacetime is the Bit', I'm not sure you're that far from the Weizsäckerian picture, in particular when you're talking about Stern-Gerlach measurements.)
Coming from the quantum side of things, I must confess that any attempt to 'geometrize the quantum' instead of quantizing geometry finds me a bit hesitant, but your argument regarding 'wild' embeddings as deformation-quantized versions of tame ones is nevertheless intriguing, I'll have to think about it for a bit. Maybe there's a sort of dual perspective thing here: you can start with the quantum, and get a 3(+1) dimensional spacetime out, or you start with the spacetime, and out pops the quantum (via a suitable embedding). That's probably a bit fanciful, but that way, everybody gets what they want...
Anyway, I've got to go now, it was a joy reading your essay, and I hope you do well in the contest!