Your agenda and hell-bent slant is to bypass Title IX. That's the piss in your Cheerios. That's why you're contorting so hard here, in order to keep money that is solely derived from the value of broadcasting football games out of the hands of golfers, cross-country runners, and softball players.
In all honestly, I don't disagree with the spirit of that.
That said, trying to fight student-athlete employment is the completely wrong tree to bark up. Your fight is elsewhere.
All of everything said, I actually agree that it makes sense on a lot of fronts for football players to be employees of and paid by the conference, not the school.