How about this.. You hire Perlman's replacement now. Let him walk the halls of the Admin. and loom over Harvey like the spectre of Death, kind of like they did with Eichorst before TO finally left. You have that incoming hire put strong indicators into Eichorst's ear that if he doesn't pull the trigger on MR &Co. now, he's done like a dinner as quick as the hand-over takes place. I think SE is enough of the self-serving type to drop MR like a hot rock, hell it's not his money.
Then, you steer SE's hire to your preferred candidate while keeping in mind an AD replacement's ability to get along with said hire. Upon hand-over you can SE anyway, and then publically state the reason as a dislike for the hiring carousel and how it reflects poorly on the university, "Not the Nebraska Way" and all that. You get your coach, you get your AD, and HP & SE get to take the stigmata with them as they leave.
Yeah, kind of cut-throat, but needs must.