Whisk together the first 4 ingredients in a small bowl until well-combined.
In a large zip-top bag, combine squash, green onions, and sauce. Toss bag until squash slices are coated with sauce. Put bag in refrigerator, tossing hourly, for 4 hours.
Lightly oil grill and heat to medium. Lay squash slices on grill and brush with leftover sauce. Cook until browned on bottom, about 4 minutes. Turn over, brush with remaining leftover sauce, and cook for another 4 minutes (or until browned).
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