Dear John,
you present an intriguing approach, and choose an original way to attack the omniscience of Laplacian demons---I have not previously come across the Reeh-Schlieder theorem used in this way. To me, your discussion of what can be known, what answers can be obtained suggests an approach to doing science that's in a sense top-down: you formulate constraints regarding knowability, and then figure out the laws supporting such a structure. This is similar to how you can formulate thermodynamics in terms of what sorts of machines can be actually built---propositions like 'there is no perpetuum mobile of the first kind' could find their analogues in 'there is no universal prediction machine', or something more precisely elaborated. I think that's an intriguing direction to pursue!
As for the knowability of the world, you dismiss the idea that we understand what we understand, because that's just the understandable part---and in a sense, you're right that it's trivial. But I think that a part of this is that certain problems allow for radical abstraction, while others don't---at least, not without some loss of the original question's spirit.
Consider Königsberg in the early 18th century. Immanuel Kant, on one of his clockwork walks, traverses the bustling city, perhaps exchanging greetings here, perhaps pausing a little there, maybe mulling over something intriguing he'd read in a recent publication of David Hume there, walking back and forth across the famous bridges. Can he traverse the city without crossing a bridge twice?
The problem, of course, has a simple solution---and for that solution, we practically disregard everything about the tale above. We need not mention Kant, the way he walks, what he thinks, or even Königsberg, at all: we can simply translate the problem into a simple question in graph theory, and answer it in the negative. The crux is that nothing is lost in the translation: the graph theoretical problem models the question about Kant's morning walk exactly. The mathematical description is not merely an approximation, it is precisely equivalent---this is something sometimes missed by those who claim that mathematical laws in physics have only an approximate validity.
Hence, problems of this kind are simply, and exactly, solvable with finite, and radically limited, resources. Many problems are of this kind, or sufficiently close; but others may not be. So I'm not quite sure I agree that we 'have a working framework for understanding literally everything'. In fact, it often seems to me that we have a framework for only the really easy problems---what the world is made of, how the simplest things interact with each other. Physics, chemistry, biology---not to diminish the success of either, but I think in a way that's the easy part. The hard questions are, at this point, not even precisely formulated---what is good and right, how to live a good life, how to build a just society, and so on. I think there remains much we don't know about any of these issues.
But then again, we've only been at this for ~10,000 years, give or take, so it shouldn't really surprise us that we're only getting started at the difficult stuff.
You also seem to kinda renege on this point when you describe the behavior of people as 'effectively random'. In fact, it's very far from random---even in a technical sense: if you ask a person to come up with a random sequence, it's fairly simple to write a prediction algorithm that takes past performance to predict the next number with significantly greater than chance success. It's something we rely on every day: many of our interactions with our fellow humans are predictable to at least some degree; we typically know what to expect of our peers. There are surprises---more or less pleasant ones---but they're surprising precisely because they're relatively rare, and typically still fall within a fairly narrow domain of human behavior. Somebody might deny you a request you thought reasonable, but they won't strip naked and start flinging poo. (Unless you happen to be stranded in a YouTube-comment thread, perhaps.)
Finally, I think the notion that whether we should think of something as true depends on its verifiability is somewhat difficult. First of all, it's required for verifiability to be meaningful that there are independent truths to be verified---if you predict that A, and observe that A, for this to be a verification it must've been the case that A, whether or not you made the prediction or experiment to actually find out that A. This holds even in cases where you can't actually carry out either the prediction or the experiment itself.
Additionally, it's vulnerable to skeptical arguments. You could always be just a brain in a vat, being fed appropriate sensory data. You can never exclude this hypothesis, and hence, never carry out a strict verification; but then, we would never be able to speak of anything being strictly true or false.
But these are minor points that I feel deserve some additional consideration. Your overall approach is, I think, a valuable and interesting one, and I'm happy to have discovered your essay before voting closes. Wish you best of luck in this contest!
Cheers
Jochen
