most people seemed to think Snape and Hamlet would hate each other on sight, but I think they just might have a few things in common

I don't think that these are mutually exclusive options ;-)

This is brilliant - I look forward to seeing what happens next.

(Cambyses, King of Persia isn't the one that rips off all the lines from Hamlet is it, or was that a dreadful play about Alexander instead?)