In glass or ceramic casserole dish, whisk together miso paste, cider, soy sauce, garlic and ginger. Add fish, skin side up; cover and refrigerate for 6 hours.
Lemon Thyme Vinaigrette: In bowl, whisk together oil, cider, vinegar, shallots, thyme, maple syrup and salt. (Make-ahead: Refrigerate for up to 6 hours.)
Remove fish from marinade; brush with oil. Place on greased grill over medium heat; close lid and cook, turning once, until fish flakes easily when tested, about 10 minutes.
In bowl, toss greens with vinaigrette; divide among plates. Top each with fillet.