I agree that for UK universities your application needs to show your passion and commitment to the subject for which you are applying - within the limitations of what your school offers.
If AP Latin is not available, then what is? What other history or essay based course is available, either at school or at comm college?
Taking DE in sports management does NOT show this level of commitment. I would choose another, more relevant DE course, ideally one that hones your research, reading and writing (esp long form essay) skills.
What additional reading do you do outside the school curriculum?