Brohm would be a nice choice, although he doesn't strike me as having any interest in KY.
Schiano actually might be a nice fit. He built up a Rutgers program to respectability, which is pretty damn tough to do. Don't think he's great, but probably a decent fit for what needs to be done.
Guys like Briles or Tressel would obviously be awesome. Both can really coach. Of course both have their trouble. I'm fine with that. I'll risk trouble for a better team. But to me the biggest problem with getting either is that when they get past their sanctions and their troubles have blown over, some school with more allure will take them.
And I still like Butch Davis. Longtime Hurricanes fan for decades, as well as KY. The man can recruit better than anyone imo. Doesn't recruit just 5 stars like Saban because of Bama name, he's always been adept at pulling 2-3 stars that could play (like Ed Reed) and developing them. He stocked a roster at UNC with NFL talent. Built the single most talented roster ever in cfb at Miami coming off probation. He's been wanting to coach and practically begged for the Miami job. Obviously, he wouldn't have the same interest in the KY job, but I think he would take it. But also from following him in those Miami years, he earned the nickname Botch from the fanbase because of his brainfarts on the sideline, so he would carry some baggage of not being a good gameday coach. But he would recruit better than Stoops, and would have a physical, fast team that darn sure didn't play timid.