Killing the agencies and the Civil Service and the 17th Amendment is a minimum necessary to regain the Constitutional Republic. Anything less buys a hiatus of shorter or longer duration at best in the march to the Total State. Repealing the 16th and 19th would put firmer ground under a reclaimed Republic.
The Civil Service was instituted to combat the evils of the Spoils System that saw the crooks ejected and replaced with more crooks with every change of Presidential Party. The fact that that needed to be changed is evidence that the bureaucracy was far too large already for long continuation of the Republic but the Spoils System at least kept the bureaucrats from becoming entrenched to grow to be the major power in the nation.
You need to at least get your people you trust in place to even determine how the downsizing can be done. There are people at the other end of those phones that all those staffers spend their time on — the public, local government bureaucrats, etc. To avoid chaos, things need to be shut down in an orderly fashion, which takes time.
There may be no downsizing desired at the FBI, NSA, CIA, Homeland Security, etc. which is where some of these leaks obviously originate, so simply shutting down those agencies isn’t a way of stopping leaks.
Although their jobs may ultimately go away, there may be a large majority of those workers that are not ideological, just went into government because it was a good job. I would ask those “good people” to squeal on their fellow employees if they know anything about leaks, foot dragging, obstruction, etc. Co-workers usually know how their fellows are behaving and misbehaving. Offer them rewards for turning in the bad apples. Even if they know their job is going away, a bonus in the meantime is still going to entice them.