Hi Stefan,
thank you for your comments. Unfortunately, I don't have time to reply to them in full right now, but I think there's a potential misunderstanding here that I wanted to try and head off.
In a nutshell, my proposal is that the world, as such, is non-computational---indeed, I view computation ultimately as a subjective notion: a system computes only if it is interpreted as computing something. This isn't really different from other symbols (since ultimately, the states of a computing system are just symbols). A set of cracks in a rock made by natural processes a billion years ago, before any humans were around, has no meaning, even if it happens to spell out something (indeed, I remember the case of an alleged runestone turning out to be just such a natural phenomenon; nevertheless, a 'translation' of it had earlier been proposed).
However, our minds use symbols, and---if my two propositions are right---perform computations. For this to be possible, this computation must be underwritten by a process that is not itself computational---otherwise, we'd end up in an infinite regress. The hypothesis that it's qualia that underlie this mental computation then serves to ground it, and also explains why qualia are such a challenging concept---because we can't make computational sense of them. (Note that it doesn't mean qualia are all there is to consciousness.)
So, in brief, we use computational reason, modeling, to try and explain a noncomputational world---which is only ever possible partially. This is not such a radical proposition, really: it's the situation we've been in with respect to mathematics ever since the Gödelian incompleteness theorems. There, things are often phrased as if they're a problem for mathematics---'mathematics is incomplete', or something of that sort. But really, they're just a problem for mathematicians: because human mathematicians are limited to effective, formalizable means, no axiomatization we could come up with can encompass 'all of mathematics'.
If I'm not completely off-base, then the same thing holds of the physical world: no model ever encompasses it completely. Consequently, holding any particular model's base facts as 'fundamental' is just as misguided as thinking of any particular set of axioms (that are accessible to human mathematicians) as 'the axioms of mathematics'.
As for determinism, that's actually an interesting question I didn't have the space to engage in the essay. Basically, you can represent every noncomputable function as a computation augmented with a string of random numbers (see, e.g., here). Consequently, a computational reason, faced with a noncomputational world, could at best understand it as some deterministic evolution with interspersed random events---which is of course exactly what we actually have in quantum mechanics. So here, too, the hypothesis that we're trying to apprehend a noncomputational world with computational means seems to hold some intriguing explanatory potential.
To me, this seems then a fairly simple idea, with precedent in pure mathematics, that serves to elucidate many otherwise puzzling features of the world.
I'll try and get back to some of your more in-depth remarks and questions when I have more time.