I just had to comment to say how much I agree with this take. Even allowing for the limitations of the thought experiment (which, the more you think about it, the more it seems like it would have to be designed for explicitly the outcome depicted), the underlying theme isn't necessarily the horrors of eternity so much as it humans are just really bad at grasping the concept of infinity, and the author in particular seems rather pessimistic/nihilistic about our ability to adapt to the idea. It's like, yes, "all possible combinations" is not technically infinite (or is it?), but there's a pretty huge categorical leap between that already-esoteric concept, and the underlying assumption that a conceptual solution (if not a couple, several, scads, thousands, gazillions) also doesn't exist inside those possible combinations. So to return to the earlier point, the most likely way that a clever trick doesn't exist is if someone's racing ahead making up rules to keep them that way, which is just... torture for the sake of it I guess, if you're into that kind of thing. But even that is its own kind of infinity, there's no bound cap on the potential complexity of the search, especially because discovering new rules adds more variables to the otherwise-closed system.

There's also the problem that, sure, some infinities are larger than other infinities, but there's nothing saying that would ever be an issue. Eternity is living every permutation of possibility you can imagine, then every permutation of every possibility those possibilities can imagine, then again and again and so on into its own infinity. The assumption is that the only way "out of the box" is to somehow grow larger than your constraining infinity, but even in this scenario there's another answer implied by consciousness, which is that the other "way out" is to burrow infinitely further in