Need to fill up your inventory, so it can't fit, and either put it on your mouse cursor (pick it up) and pick up something else and go to another zone, or open up a blueprints (if you have one) and fix your inventory so it can't fit anymore, then close the blueprints. Either should make it drop. It's worth it to keep one set of blueprints on you just so you can force broken quest items to drop.