Hello, @bluelavender.
I enjoyed your concept, so, I will give you a piece of advice, that I ask you take not as criticism but as help for future works, or a rework of this same text, because the concept is worth it and it could be easily expanded upon. Considering the persons mentioned as the best writers in the world may be a matter of opinion, when so many and so good were left out, starting with the first casualty, the poet Valmiki, who wrote the Ramayana and is probably the most copied of them all, not only because he wrote the first impressive piece of epic poetry, but because he is the oldest one. You can't depart from Homer skipping Virgil, or Rudaki, the persian; nor talk about the german Dante and the italian Petrarch and skip the portuguese Camoes. To make the logical jump into Poe, skipping Cervantes, Dumas, Victor Hugo, Tolstoi, Lovecraft, Verne and Conan Doyle... I believe I could go encyclopedic here... And this is just to make a point about the importance of solid research, but that, is not the most important. Three main things matter when you write something that is to be read by others. The first one being what Homer would call "Virtue", and that I call intelectual honesty: this means you must not generate resistance to your writing, in the readers mind, by presenting statements that he can easily fall into disagreement with. So, this would be the difference between saying "the world's best authors", saying "my favourite authors", or adding a simple "in my opinion"... Paying attention to "Virtue" is very important because it allows for the reader to take in your writing without ontological shock.
The second thing is the principle of parsimony in writing, or: the importance of not writing words that need not be there. This can include unneeded characters, repetitions of content after the point having already been made, and, in general, what William Faulkner said about wordiness: "Too many words dilute and blur ideas". So, be economic.
The third, and probably most important is: never,but never, surprise the reader. What does this mean? Well... It means that, even if you don't tell the reader how you got there, you will have to leave him a hint, so he makes the logical jump himself. Albert Hitchcock famously called this instrument the Mcguffin. It is the knife that was on the drawing board when the character entered the room on the scene before, it is the strange hissing sound that later turned into a blown up tire, it is the suitcase in Pulp Fiction, that everybody chases without even being important what it contains... What is important is it is shown in a key moment and it helps the reader not be surprised, because a surprised reader is a reader that feels deceived. You must allow your reader to feel the satisfaction of saying "I knew it"! That is why I would suggest that the key to that door in Irkutsk could have entered the story much earlier, maybe in a small paragraph setting the scenery, so the reader can know where he is and be aware of the Mcguffin.
I hope you find these ideas of mine, helpful. Would you be willing to re-write the story considering what I disclosed? I would much enjoy to see you play with your story and tell it in different ways... That is also a way to improve.
To check out where playing around with the idea of meeting famous characters from our past may lead, I would suggest a read: Dead Philosophers' Cafe: An Exchange of Letters for Children and Adults, by Nora K. and Vittorio Hösle.
And remember: there's many ways to tell the same story, and @hefestus is not always right.
Keep on writing good stories,
Pedro