Steam Workshop is a great example.
I think EA would need to provide a complete working system so you can use the app from day 1, but the default replaceable components could be whatever they were going to ship in Madden anyway, just API driven and modularized. Then you take the API for, say, weekly progression, run your own code, and return whatever values Madden expects, and then you have your own weekly progression engine. EA just needs to define the APIs, allow you to override what code is loaded for it, and away you go. They'd also need to provide the official "app store" and the workflow that reads and writes the save game files.
The system would be limited by the APIs offered, but it's a start and a solid foundation going forward - something that can be improved upon in an Agile manner outside of Madden release dates, because it's simply about reading and writing the franchise save game files, which can live somewhat independently from Madden version, to an extent.
It's a tall order and realistically never going to happen, but it's a tried and tested way to solve problems like this.