Not to rain on the parade of your enthusiasm, but it all fell on deaf ears before. They do have a tight relationship, at this point.
Try to find which owner is under NFL Branding and Video Gaming? And I am sure it is an NFL owner.
The NFL won't be open to other options besides EA. As was explained before in another thread, the NFL makes more money off one publisher vs 4 publishers. And, based on past history, they won't blow up their business model of exclusivity success over a petition.