Its not just exclusives. Im a firm believer this game has different loot tables for every account. In 1200 hours, I've pulled 29 gallys, 7 hawkmoon, 9 suros, and duplicates of every other exotic. But my unicorn is the red death. I've never EVER had one drop. It seems your unicorn is the hawkmoon. I even know one guy that has never had a NLB drop, which for me happens just by logging in, lol.