I would actually create a new cabinet position. I don’t know what you would call it but its position would be used too look at government agency’s for the purpose of eliminating bureaucracy. the idea being that it is hard for agency’s to shrink themselves. you need an outsider agency to decide when money and resources are being wasted and personnel and departments should be cut.
How about Department of Departments (DOD.)
Reminds me of a scifi short story I read decades ago, where the main character proposed creation of a "List of lists," since no one could remember what they all were. His suggestion was approved, and an entire government department was created, to handle that important function.