Nonfat dry milk substitution?
I would just sub in soy milk (or other nondairy milk) for the nonfat dry milk plus some of the liquid. I very often sub in milk for nonfat dry milk in yeasted sweet bread recipes... Even in my favorite recipes I've made a hundred times, I see very little discernible difference in texture or flavor.
To figure out how much liquid to sub out, typically 1/3 cup NFDM powder plus 1 cup water makes a cup of "milk."
So I make a sweet roll recipe which calls for 1/3 cup NFDM powder and 2 cups water elsewhere. To sub, I'll use 1 cup milk and 1 cup water.
Good luck; I imagine it will turn out completely fine!!!
When I used to do a lot of vegan baking, I found that rice milk powder worked better as a sub for milk powder than soy powder. It dissolves more quickly in the wet ingredients -- soy milk powders can stay a bit grainy. Better Than Milk makes a pretty good version of both soy and rice milk powders. They're pretty expensive though, especially for a one-time bake, so it might make more sense to just sub soy, rice or almond milk and reduce other liquids as nothingswrong suggests.