I'd look at the following guys, in this order.
1) Joe Brady, Carolina Panthers OC. 31 years old, college coaching experience at William & Mary, Penn State, and LSU. Sean Payton disciple who specializes in passing game/QB's.
2) Brian Daboll, Buffalo Bills OC. 45 years old, college coaching experience at William & Mary, MSU, and Alabama. Belichik and Saban disciple who has worked wonders for Josh Allen- and really developed him into a QB that looks like he could take his team to the playoff and be a legit MVP candidate.
3) Kellen Moore, Dallas Cowboys OC. 32 years old, one of the all-time, record setting college QB's, no college coaching experience- but his offenses in the NFL are known for their creativity and puts up huge #'s. Never had the talent or size as a player- but his mind and knowledge of game was supreme- which is what made him great as a college player.
I'd go after one of those guys. And then I think I'd go bring Greg Mattison as Co-DC and give him a huge pay raise and then hire Chris Partridge as Co-DC- and let those guys build a staff together.
Michigan's downfall on defense was losing Mattison and Partridge. Mattison was their 2nd best recruiter behind Partridge- and he developed all those DL recruits into solid players- guys like Frank Clark (2nd rd pick- would've been 1st if not for assault charge/program dismissal) Chris Wormley (3rd rd pick), Taco Charlton (1st rd pick), Chase Winovich (2nd rd pick), Mo Hurst (5th rd pick- blows my mind he went this late- he shoulda been a 1st rd pick), and Ryan Glasgow (4th rd pick). And Partridge was the primary recruiter all of their top rated recruits like 5* Rashan Gary (1st rd), 4* Devin Bush (1st rd), 4* CB David Long (3rd rd pick), 5* Aubrey Solomon (transferred), 5* Chris Hinton (still a young pup), 5* Dax Hill (still a young pup), 4* Ambry Thomas (will def be drafted- just don't know where).
Don Brown is getting exposed without a guy to develop DL like Mattison can, and without a guy to recruit future NFL draft picks like Chris Partridge can. When Brown goes against offensive teams with equal or more talent to what his defense has- he gets exposed- because he can't scheme. His scheme sucks. This is his scheme: man to man across the board and blitz every down!