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Sounds like a 13" x 9" to me - they would be too thick in a square 8x8 pan. For flavor and texture I wouldn't sub water for the milk, though you could reconstitute some nonfat dry milk powder in water and use that. The milk to flour/sugar ratio sounds about right, but the oil seems like a lot...let us know how they turn out!
Why not use almond, soy or coconut milk, unsweetened variety if you don't want the extra sugar? I love to use these milks in baking. They even curdle with apple cider vinegar - just like cow's milk - to use in place of buttermilk.
Just to clarify, I reflected the change in oil/fat amount in the recipe--i started with half and worked up to the right amount.