Combine first 9 ingredients in a large zip-top plastic bag; seal and marinate 30 minutes. Remove mushrooms from bag, reserving marinade.
Prepare grill or broiler. Place mushrooms on grill rack or broiler pan coated with cooking spray; grill 6 minutes on each side or until browned, basting occasionally with reserved marinade. Spread 1 1/2 teaspoons Roasted Red Bell Pepper Sauce over cut sides of rolls. Place 1 mushroom cap on bottom half of roll; top with 1 cheese slice, 1 lettuce half, 1 tomato slice, and roll top. Repeat procedure with remaining ingredients.