Baking – How to improve the flavor of gluten free challah bread

I wouldn't replace milk powder with vital wheat gluten. Vital wheat gluten changes the gluten content of your recipe. It's good for, say, turning whole wheat flour with a lower gluten content or AP flour into flour suitable for bread.

When I add vital wheat gluten, I subtract flour as your friend does. I only use it when I am not using a high protein flour.

The dried nonfat milk powder is likely in the recipe for flavor. I would instead use milk in place of water and either up the flour as needed or replace with flour as needed (you can tell this during kneading). I've done this just fine in bread recipes before.

In an answer to another question, someone else was looking for answers on dealing with thickening dairy. If you want to address thickening with corn starch, here are some beginning steps;

• Use the right ratio of corn starch slurry to liquid: 1 tablespoon corn starch thickens 1 cup of liquid
• Use the corn starch in a slurry: although you didn't mention clumps (which slurrying prevents), I mention this as a best practice for many applications - whisk the corn starch in an equal amount of cold water then pour in slowly while stirring the pot
• Heat the corn starch through: you need to heat the liquid until you can no longer taste the starchiness. Unfortunately with a bechamel boiling isn't preferable, but heating it for an extended period of time at a high temp will cook away the starchiness

Although I understand you are looking for a common thickener, be aware of the possibilities as you may have one on hand one day from some other purpose. If the three steps above don't solve your problem, I think that you may be putting in more effort than just buying some more apt thickener. Even so, corn starch should do fine, it sounds like the problem may just be in the completeness of your preparation.