Whisk marinade ingredients in a bowl until sugar is mostly dissolved. Place salmon filets into a large ziplock bag and pour marinade over top. Seal bag and allow to sit in marinade for 10-20 minutes.
Heat an indoor grill pan over medium heat. Reserving the marinade, grill fillets on both sides until nice grill marks are achieved and salmon is cooked to medium/medium-well. Skin can be easily removed after grilling. [Or see notes for broiler instructions]
Heat reserved marinade in a small saucepan on the stove until it comes to a simmer. Spoon sauce over salmon and rice. Garnish with lemon wedges.