Lori, I can relate to your woes. It is a shame when “bean-counters” without medical knowledge or background make life-saving, quality of life decisions instead of our medical care teams.
How is your son doing? Not just with his T1D but with life, school, activities and social? At age 14 an insulin pump should be a major step that will permit him to lead a full, productive life, giving him freedom for meal-timing changes to fit in with schooling, sports and just being a teen. Those are a few bits you could add into your appeal.
The first step is to engage his medical care team behind you, especially an endocrinologist who really knows TyoeOne [not all really do]. Have the endo write the appeal stating why, in her/his judgement that a pump IS NECESSARY; also engage an instructor / medical advisor from the Omnipod company to assist with additional data.
In retrospect, if I had the positive benefits of a pump 60 years ago I may not have developed some of my diabetes-related complications. Good Luck to you!