I now have also made her ham and cheese and grilled cheese sandwiches, which she is devoured. I haven't had much luck getting her to eat bread or toast. But she ate all the bread with her grilled cheese and a hamburger bun with her ham and cheese sandwich. So, I am actually getting a little more grain in her. Also, the bread I buy has milk in it, which she tolerates in baked goods. I like being able to give her a little milk as much as I can even if it's not directly given to her. I think it will help her build up a tolerance.
I'm going to do a little more research and see if I can find another soy-based cheese for her that might contain a few "better" ingredients. Otherwise, for now I'm happy she's finally eating this cheese and bread