Suggestion from my experience as a 17 year lead mentor, FRC Regional Planning Committee Co-Chair, and high school engineering instructor. Prepare by reading this:
NCAA Study. Then download and read this
Brandeis University Study
Then formulate a presentation highlighting the importance of a balance of traditional and "hands-on" education (your 'applied STEM') with sports. Your thoughts to work with the Principal should be kept up front as "buy-in" from this individual is a top priority. Make sure you understand what the principal's point of view is as well, with an open mind. Ask many questions.
Seek community support from alumni, parents, sponsors, board members and make sure that they are all using a similar message - FIRST is a fantastic program for instructing students to use their minds and hands to learn tangible, transferable skills.
Best of luck! It is worth the effort!