I have my top 3 finally figured out- Dave Clawson, Luke Fickell, and Matt Rhule. All a proven winners who have rebuilt programs. All have extensive head coaching experience and all 3 coach great fundamental football. Listed below in random order. I would be happy with any of them.
Matt Rhule - 47 years old
Temple
2013 - 2-10
2014 - 6-6
2015 - 10-4
2016 - 10-3
Baylor
2017 - 1-11
2018 - 7-6
2019 - 11-3
Left for the NFL
Dave Clawson- 55 years old
Fordham 1999-2003 - Winless in 99 to 10-3 and 9-3 in 2002 and 2003
Richmond 2004-2007 - 3-8 in 2004 to 11-3 in 2007
Bowling Green
2009-2013 - 6-6 in 2008 to 10-3 in 2013
Wake Forest 2014-current - 3-9 in 2014 to 11-3 in 2021 and is currently undefeated in 2022
Luke Fickell - 49 years old
One year at Ohio State under weird circumstances - 6-7
Cincinnati 2017 - current
2017 - 4-8
2018 - 11-2
2019 - 11-3
2020 - 9-1
2021 - 13-1