I heard a discussion on talk radio yesterday about the decline of the NFL. In this discussion, the tangents included that kids are forgoing football for other sports growing in popularity in the US. Specifically, the rise of lacrosse was mentioned. Now, I know that doesn't equate to the topics introduced in this thread, which I think are interesting arguments and worth examination. But I don't think that even assigning a mulitiplier for the number of disadvantaged students is going to have a significant impact on "leveling the playing field". For instance, Iroquois High School (used in your proposal), is a school with one of the highest ESL students. However, that doesn't necessarily preclude them from being able academically or physically in playing football. What you do have, though, is a huge cultural difference in the sports that are preferred. Given low numbers of participation, and the increased costs of transportation for a school that already struggles to field a team, I wonder if this would bring about the end of football as a sports choice at that school.
I understand that there are differences in the challenges of public, private, independent, rural, urban, open enrollment, district bound enrollment. But I don't think reclassifying based on the economic demographics or the demographic of learning differences accomplishes anything other than to bring a negative connotation in association with those schools, especially those with enrollment heavily skewed toward the disadvantaged circumstances of their students.
I think before we consider reclassification of a sport based upon such factors, we need to examine the full scope of what that means in a larger context. In the overall scheme of things, the educational experience is the most important consideration when talking about schools. The educational experience includes extracurricular participation, but does not necessarily mean a powerhouse program.