Create a two-zone indirect fire in grill by banking charcoal on one side. Alternately, light only half the flames of a gas grill set to high. Stack 2 large pieces of heavy duty aluminum foil and fold edges up to make a cooking tray for fish.
Whisk egg whites to soft peaks. Fold in salt, cilantro, and 1 cup parsley. Place thyme and citrus slices in body cavity of fish and set aside. Place 4 tablespoons egg white mixture onto foil tray. Place fish on top and spoon remaining mixture over fish, making sure to encase the entire fish, creating a seal. Transfer to indirect heat on grill and cover. Cook for 25–30 minutes. Remove fish from heat and let rest. Combine cooked quinoa, carrots, zucchini, tomatoes, lemon juice, ½ cup oil, and remaining 1 cup parsley in a large bowl. Mix well. This can be made one day ahead. When ready to serve, transfer tabbouleh to a serving dish and top with feta.
To serve fish, strike crust with the back of a spoon to crack. Use a knife to carefully remove salt crust from top of fish and scoop flesh onto serving dish. Drizzle with remaining ½ cup oil and garnish with lemon and dill.