Does the milk in icing do anything other than add water content? Could you go with maple syrup instead of milk (adding in some powdered milk to make up for milk solids, if they're needed for something)?
Since maple syrup is a bit thicker than milk, I think the icing would be too dense and would be worse if you added milk solids.
That said, I would be inclined to replace some of the milk with maple syrup and then adjust the milk and/or sugar to get the right thickness, rather than using extract.