I was familiar with Parmenides' thesis since I have had a course in pre-Socratic philosophy. Your take on Hamlet's famous statement sounds plausible as well as your justification for this interpretation. Is Hamlet's statement that "There is nothing either good or bad, but thinking makes it so." occurring in the play nearby the more famous quote about being, or is there something else in the nearby context to suggest that Hamlet is still thinking of that?