Your second solution depends on interpreting the "Albert knows Bernard doesn't know" to mean that Bernard told (or otherwise signalled to) Albert that he doesn'

Your second solution depends on interpreting the "Albert knows Bernard doesn't know" to mean that Bernard told (or otherwise signalled to) Albert that he doesn't know, rather than Albert deducing that Bernard couldn't know. There was a detailed rebuttal of this interpretation by the folks who set the original question. But it is easy to claim "that's not what I meant!" Actually being precise about what you mean is fiendishly difficult. I recommend Imre Lakatosh's excellent book on proofs "Proofs and Refutations" - its short, and thoroughly dismantles the early 20th century ideas that math is somehow a precise conceptual structure independent of language ambiguities. Or put another way: with enough eyeballs, all language is ambiguous.