Microwave scallions in a loosely covered pie plate on HIGH for 1 minute to soften.
Place each steak between sheets of plastic wrap. Gently pound until about 8x6-inches and 1/8-inch thick. Lay 3 scallions down length of each piece; tightly roll up from a long side. Secure with wooden toothpicks. Put in a large ziptop bag.
Stir sauce, sugar and water in a microwave-safe bowl until sugar dissolves. Add 1/3 cup of mixture to bag; refrigerate 30 minutes or up to 1 hour.
Heat outdoor grill or stovetop grill pan. Grill negamaki 5 minutes, turning to brown on all sides. Discard marinade.
Remove picks; trim ends of negamaki, then cut alternately straight across and diagonally in 2-inch lengths.
Microwave sauce in a bowl to heat; serve with negamaki.