I don't think it's going to be as difficult as you think. There's only 32 of these jobs on the planet, we can get a good coach.
Three reasons why the Redskins will not get a guy like Shaw or Jim Harbaugh:
When you're a college coach, you're essentially a god on campus. The players have none of the egos (and none of the associated power) that the pros do.
If you're a Power 5 coach, you can get a number of wins just by recruiting players better.
If you're going to go the pros, you aren't coming to a team that has a managerial dumpster fire in charge.