In a food processor or blender, combine wine and 2 cups berries; whirl until puréed. Rub berry mixture through a fine strainer into a 1 1/2- to 2-quart pan; discard residue. Add shallots, ginger, and 2 tablespoons sugar. Bring berry mixture to a boil over high heat, and stir often until reduced to 1 cup, about 10 minutes. Remove from heat, and stir in butter and more sugar to taste (see notes).
Rinse salmon and pat dry. Coil belly strips of fish into center of steaks and secure each portion with a small skewer (such as the kind used for trussing turkeys).
Lay salmon on an oiled grill over a solid bed of hot coals or high heat on a gas grill (you can hold your hand at grill level only 2 to 3 seconds); close lid on gas grill. Cook fish, turning once, until opaque but still moist-looking in center of thickest part (cut to test), 7 to 10 minutes.
Set a salmon steak on each of 6 warm plates (remove skewers if desired). Spoon berry coulis (if cool, stir over high heat until warm, about 1 minute) equally over steaks. Garnish with remaining 1/2 cup whole berries; add salt and pepper to taste.