Reconstructing Shakespeare

Dear Prudence,
My girlfriend and I are having a disagreement. I posed to her the following hypothetical situation: Would you rescue from fire and certain destruction the last surviving copy on earth of the complete works of Shakespeare or a single puppy? My girlfriend says that she would rescue the puppy because the puppy is a fellow living being. She is highly educated and claims to have great respect for Shakespeare. But I think my girlfriend’s choice is the wrong one. I would rescue the Shakespeare, not just because of the aesthetic enjoyment we get from his work but also because of all the moral insight it provides us (including possibly the insight that enables the concept of animal rights in the first place). We’ve argued a lot about this. I cannot take her answer seriously, but I find it rather disturbing nonetheless. She never rejected the hypothetical question out of hand or said that the two things aren’t even comparable. She says that preserving a living conscious thing is more valuable than preserving Shakespeare. My girlfriend loves animals, especially her poodle, and is a die-hard vegetarian. I am, on the other hand, obsessed with Shakespeare and rather neutral toward animals. What is the best way for us to diffuse this situation?

A silly letter, to be sure.  But this got me thinking: if we lost all written copies of Shakespeare, could we reconstruct it?

Of course we could.  There are enough people wandering the earth right this minute with bits of Shakespeare memorized that we could get it back within a matter of hours.  Just reassemble all the most recent casts of every play, have them perform their parts, record and transcribe it, you'll be done before last call.

So let's make this harder: we've lost all written copies of Shakespeare, all living people have lost any knowledge or memory we've ever had of Shakespeare (to the extent that we don't even remember that we've lost it), and we've also lost all academic and educational works dedicated to the study and analysis of Shakespeare.  Could we reconstruct it?

We could certainly get a lot, because Shakespeare is everywhere.  The plot of Hamlet was reiterated in the Simpsons, Archie comics namedrop "wherefore art thou" and "to [verb] or not to [verb], that is the question", and Shakespeare is specifically mentioned in many works in all different kinds of media.

I even once read a young adult novel that explicitly stated that West Side Story is a modern adaptation of Romeo and Juliet. So from that one book that I read in elementary school alone, the people of this mythical post-Shakespearean people will learn that there was once a play called Romeo and Juliet with a plot vaguely resembling that of West Side Story.  Surely there must be other works that specifically mention that something is from Shakespeare too.

This post-Shakespearean population would also quickly catch on to the fact that "wherefore art thou" and "to [verb] or not to [verb]" sound like they come from something, and that a guy talking to a skull and a guy with some kind of disability saying "my kingdom for a horse" are somehow existing tropes, and scholars would try to trace their origins.  I wonder how much they could reassemble?