I've read a lot of speculation that Kelly was a poor hire to begin with because he lacked major program experience, and that made him incapable of achieving consistent high level success at ND. The argument that Kelly did well at Cincinnati with weak talent has been used against him by many, saying that he doesn't know what to do with elite athletes (not sure I agree with that last part, but it's an argument that's been made).
If that is the case, then we should look for someone who has been an assistant at a major program and then had some relative success as a head coach in a P5 conference.
Whittingham did a solid job taking over for Urban at Utah, and that one special season in 2008 is a huge feather in his cap, but in the four years since they joined the Pac 12 they have not elevated their program. They have finished 2nd to last in the Pac 12 South (only ahead of pitiful Colorado) 3 consecutive years, and this is the first time in 3 years that they were even bowl eligible. Sure, they've had some occasional upset wins but so has Northwestern, and 4 years in they're still closer to the cellar of their conference. Even his 2nd best team at Utah got dominated by a 4-5 ND team.
By comparison, Gary Patterson also lacks major program experience, succeeded in the Mountain West, won a major bowl game, and struggled initially after upgraded to a P5 conference. But unlike Whittingham, Patterson got his program back in the Top 10 in only his 3rd year after the conference upgrade.
So to answer your question, I would target Patterson before I would target Whittingham, and I'd look at a lot of other guys that have had more success than Whittingham has in major conferences (Dantonio, Mullen, Gundy, and others). But that's just my opinion. I think the larger point is that after Saban/Meyer/Stoops, there isn't a candidate out there who doesn't have some flaws in his resume.