You can find juniper berries in the dried-spices section of your grocery store. (They are sold whole.) Crush them with the bottom of a saucepan, the flat side of a knife, or a mortar and pestle.
Stir together dill, sugars, salt, gin, juniper berries, peppercorns, and orange zest in a medium bowl.
Place a large piece of plastic wrap on a rimmed baking sheet. Place 1 fillet, flesh side up, on plastic wrap. Pour dill mixture over fillet, and press lightly to coat. Top with second fillet, flesh side down. Wrap tightly with plastic wrap.
Place baking sheet on bottom shelf of refrigerator. Place another baking sheet on top, and weigh down with several plates, cans, or even rocks. Chill 24 hours, turning wrapped fillets at least once.
Unwrap fillets. Place fillets, flesh side up, on a parchment paper-lined baking sheet; chill for 12 hours.
Preheat oven to 375°F. Brush bread slices with melted butter. Bake in preheated oven until lightly browned and crisp, 3 to 5 minutes. Let cool completely, about 5 minutes. Slice fish diagonally into paper-thin slices. Top each bread slice with 2 fish slices and 1/2 teaspoon each mustard, cornichons, and chives.
Total 36 hours, 15 min., including 24 hours chilling and 12 hours standing