This is most excellent!! I've already bought and read it -- and enjoyed it quite a lot (I've enjoyed it even further when I went back and noticed some references I had missed, like "M" and "N", heehee)

The good thing about Shakespeare (as opposed to Harry Potter) is that all rights are expired and so you would be free to try and professionally publish this, if you want -- though I wonder if just naming it "Hamlet and the Philosopher's Stone" may make it more marketable as a parody.