As opposed to the Congressmen who are famous for blabbing secrets to the media.
Exactly. The first step is reducing the number of people who have access to FOUO stuff (which doesn't require a clearance) or else restricting the FOUO data, and working your way out from there. Some of this stuff could easily be leaked by White House or congressional interns, for example, that are sitting in on meetings or otherwise might have access to it via making copies, etc. Also other support staff in administrative roles.
I don't know the full list of leaked stuff, but so far what I've seen has been unclassified. Which makes sense, since most people (Hillary and staff excepted) know how serious it is to leak classified data. Cleared intelligence people would be way down my list for leaks at this point. My first step would be severely restricting access to meetings and strategy sessions and fully tracking data dissemination.
Certainly a bunch of the Trump staff could use some security training as well, so they know when to keep their mouths shut. Coming in from the private sector, they're not expected to know any better initially, but they definitely need to learn.