So, Notre Dame isn't sure what to do.  My understanding is they have the following desires:

• Stay independent
• Play a national schedule
• Have the ability to compete for a national title every year
• Maintain their games with their rivals

I've been thinking about possible solutions for them & I came up with one that I think will meet all their desires with only minor downsides:  they should move to Division II.

They wouldn't have to join a conference.  Teams all over the nation play FCS teams every year.  They could compete for the FCS title every year.  They could be the FCS game each year for their current rivals.

The only downsides: Fewer home games.  Since the FCS has playoffs, they would have to actually earn the title instead just being voted in when they don't deserve it.  The last, minor downside is that Notre Dame & its fans would have to face reality that they are no longer relevant to Division I football.