I would also add to that, Moody''s character would have been an asset to Barty in how to conduct the impersonation: he had a ready-made excuse for spending as little time around others as possible, he had a ready-made vessel in Moody's famous flask to keep his Polyjuice Potion in, and any worsening of Moody's behavior (in the eyes of observers) could easily be attributed in their minds to a deepening of Moody's paranoia. Paranoid people tend to get more and more paranoid as time goes on, that is [art of why it is considered a personality disorder in its own right. He took a terrible risk stealing from Snape's office, but the Potions Master was primed to suspect Harry Potter -- and did just that. Snape also could have suspected another student first, Snape allowed the possibility that a "student" had been in his office to take ingredients for illicit brewing.
And Polyjuice might be NEWT-standard, but we are shown that second-years can brew it if they are careful and diligent.
Finally ... don't make a light joke of summary execution. Just. like, at all. Ever.