In a medium saucepan over medium high heat, whisk together the sugar, miso, sake, and mirin. Bring the marinade to a boil, then remove from the heat, transfer to a shallow dish and let cool completely. Add the fish, covering it with the marinade, and refrigerate at least 30 minutes or up to 2 days.
In a small saucepan, bring a few cups of water to a boil. Boil the garlic for 2 minutes and drain on a paper towel. In a large skillet over medium heat, cook the blanched garlic in the butter until golden, 2 min. Add the mushrooms and cook until golden, about 10 minutes. Add the lemon juice and the soy sauce and season to taste with salt and pepper. Keep warm.
Cover a grill liberally with the cooking spray and heat to medium high. Grill the fish, turning once, until cooked through, about 3 min. per side. Serve with the buttered mushrooms and steamed rice.