What is the conflict that appears in Arthur Miller's The Crucible, how is it resolved, and can you characterize this play as modern tragedy?

The play's main external conflict exists between John Proctor and society. John takes issue with his community's handling of the witchcraft accusations, attempts to address them and repair the damage done, is eventually accused of witchcraft (by Mary Warren), and dies as a result of a corrupt system. The play's main internal conflict is arguably even more interesting and occurs entirely within John. His guilt over his past affair with Abigail has eaten away at his sense of self, and John no longer considers himself a good person. His struggle to regain a belief in his own goodness eventually results in his decision not to confess a lie that would save his life. Instead, he decides to be honest and die, but he seems to consider the loss of his life to be a small price to pay for his sense of redemption.

I'm not sure I would characterize this as a modern tragedy precisely because John Proctor has ended the play, and his life, with the sense of his own goodness restored to him.  Had he compromised his values and confessed to a lie, John would have compromised himself in a really tragic way, and I would be more likely to characterize the play as a tragedy if John decided to confess the lie. To be sure, the loss of innocent life is tragic, but I would not characterize the play as a tragedy. Because John is ultimately comfortable with the choice he makes to relinquish his life in exchange for the knowledge that he dies a good man, the play seems to end in a bittersweet triumph rather than a tragedy.