So I have an alternative suggestion: Tevi Troy.
Full disclosure: Tevi is my oldest friend in Washington — I literally interned for the guy over 25 years ago. (I realize this alone could doom his prospects!)
Still, Tevi is eminently qualified. He was the No. 2 guy at HHS in the Bush administration. He has worked at the Department of Labor and inside the Bush White House and on Capitol Hill. He's also Ph.D. historian of the presidency (and frequent contributor to National Review, Commentary, the Wall Street Journal, etc.). He recently wrote the book on presidents and how they respond to disasters (a useful specialty given the recent hurricanes). And, he has an established history of flying coach when the taxpayers are paying for it!
Tevi gets along with and is respected by everybody, knows how the bureaucracy works, and is a dedicated conservative technocrat (in the best sense). Why not go with someone with no electoral ambitions and who knows how to get things done? Some of Trump's best cabinet picks have been the apolitical experts. Well, that's Tevi.