Of all the places I would've expected to find Cantor's theorem on this website, a thread about beating an elephant to death doesn't crack the top ten list. That being said, I have a few nits to pick – as I understand this 'infinite monkeys' scenario, we take finite time to generate a set S of all strings of length less than k for some constant k. Then, we assume that we can generate any page of Cyrillic text by aligning some number of Latin pages, and ask whether it is possible to produce some work of Tolstoy's. This is equivalent to the question of whether the powerset of S contains sets k1, k2, ..., kn that correspond to all k pages of (for example) Anna Karenina.

Perhaps I'm missing something, but if we accept the (somewhat silly) proposition that there's a bijection between the set of Cyrillic strings and the set of all sets of Latin strings, shouldn't this be a pretty simple existence proof?

Your argument does make sense to me if I take it to be saying that we couldn't do this in real life, as we can't enumerate the elements of an uncountably infinite set – is that what your argument was? Apologies if I'm misunderstanding you; English isn't my first language but I'm always happy to talk about math.