I'm not sure if ND's independence has much bearing. If they were to join a conference, they would probably not have a stranglehold on it. Big Ten? Nope. SEC? No way in hell. ACC? Most doubtful, as they are very top-heavy with Clemson, Florida State, Miami, and North Carolina with others such as Virginia Tech and Wake Forest showing flashes of brilliance. Possibly the Big 12, but I'm rather doubtful with their new lineup, especially BYU and Utah.
Them Mormons are mean.