ND doesn't have a program if Fleck is the next coach or anyone with similar credentials.
ND won't have any problem attracting a quality coach the next time the job opens. I'm not quite sure how you define "established big time coach" or "unproven." In my mind, there are really only 3 or 4 college guys in the country for which there would be no question about their ability to be successful and none of those will be ever coaching at ND anyway.
The names to focus on for the next coach will be current younger head coaches at the secondary Power 5 schools with good pedigrees and solid experience, i.e., Doeren at NC St, Durkin at Maryland (my favorite), maybe Campbell at Iowa St, maybe Dana Holgorsen at WV, maybe Bryan Harsin at Boise St. etc. Herman is another guy who gets lots of pub but he will in all likelihood end up at his pick of Texas/LSU/possible USC at the end of the year especially with the Big 12 not expanding.
There maybe some more 'established' guys like Mullen, Chryst , Patterson, Peterson, etc.
I'm not "recommending" any of these guys per se nor do I have any insight as to their career aspirations(i.e., Peterson is unlikely to leave the west coast, not sure Patterson is a good fit at ND, Herman will be at Texas/LSU etc) but any of them are far more 'accomplished' and experienced than anyone you can find in the MAC.