I see this post has been inactive for a while, but I was reading Hamlet the day before yesterday, and I was curious to see if my intuitions about his type were correct. However, these arguments don't make any sense to me. I would type him as either infj or enfj.
It seems clear to me that he is using extraverted feeling and introverted thinking as judging functions throughout the play. His anger is not just about his uncle killing his father, but also his moral judgment about his mother's relationship with his uncle. Someone claimed that Hamlet is indecisive and not able to make decisions quickly, but that is not true for these moral judgements.
His outward feeling judgements seem to be tempered by his introverted thinking judgements, which explains his apparent indecisiveness. He did not spontaneously decide to kill his uncle, but rather he planned it out, demanding conclusive evidence of his guilt before taking action.
I would then further argue that he is an introvert:
O God, I could be bounded in a nutshell, and count myself a
king of infinite space—were it not that I have bad dreams.
Also, Polonius mentioned that Hamlet often spent hours pacing in the room where they planned to observe his interaction with Ophelia to determine the cause of his madness.
Also remember that Hamlet is under a lot of psychological stress, explaining his subversive extraversion throughout the play.
Based on this, my first choice would be infj, and second enfj.