Is it okay to add cornstarch before cooking?
Corn starch breaks down in longer cooking so I don't think this would work well. And corn starch is an odd ingredient for a red cooked dish. I can't think of a time I've seen it used there. Usually the extra broth is kept and used for the next red-cooked dish you make and the flavors develop and improve with each use. Of course, you'll replenish the flavorings now and then to keep it in balance as well as extra water or stock
Perhaps some of the reduced cooking liquid will be served with it.