Hello, Geraldine,
The restaurants you mentioned tend to be open when the crowds are higher at the parks, and I don't know if a September visit will yield those types of crowds. However, there are still plenty of tasty choices at the Magic Kingdom.
My favorite is Columbia Harbour House with its offerings of fresh salmon, a hummus and slaw sandwich (it is amazing), and tasty soups, it isn't the typical burger and fries quick service stop. If you'd like to see a sample menu, you can click
here.
If you'd like a hamburger, Pecos Bill Tall Tale Inn & Cafe has yummy offerings and a fantastic topping bar. Here's a
sample menu of this restaurant.
If my children were to share their thoughts, they'd include Casey's Corner for hot dogs and fries. What makes it special to them is the back of the restaurant with its bleachers and vintage sport cartoons. Even as teenagers, they still have to visit here a couple of times each trip.
Please keep in mind that these are my family favorites, but there are certainly other options at the park not to mention a short monorail ride to any of the nearby Magic Kingdom resorts if you'd like to try something completely new.
Have a great trip; please let us know if you have any further questions.