Combine the pineapple juice, vinegar, ginger, soy sauce and brown sugar in a small saucepan and bring to a boil. Reduce the heat to low and simmer until the volume is reduced by half, about 30 minutes. Whisk in 2 tablespoons mustard, remove from the heat, and add the lime juice and white pepper. Let cool.
Combine the tuna, 2 tablespoons Dijon, chipotle pepper puree, honey, oil, and green onions in a large bowl, and season with salt and pepper. Shape the ground tuna firmly into 8 round uniform patties about 1 1/2-inches thick. Refrigerate for 30 minutes; the burgers must be very cold to hold their shape when cooking. Grill burgers for 3 minutes on each side for medium doneness, basting often with the glaze. Serve the burgers on buns with the watercress and the Green Chile-Pickle Relish.
Green-Chile Pickle Relish:
Combine all ingredients in a medium bowl and season, to taste, with salt and pepper. Let sit at room temperature for 30 minutes before serving so that flavors meld.