First of all - Fire 10% of the FBI staff, randomly.
Not a bad idea. Sort of the old Roman Legion idea of decimation. I’d call it decimation-lite as in the Roman Legion version of decimation one executed 10% of the soldiers as punishment.
That's exactly where my idea came from. Marine Corps basic training uses the same concept - you f** up, and the unit pays the price for not keeping you in line. Right now, there is no penalty whatsoever within FBI culture for playing politics, personal advancement, having sex with married colleagues, etc... If these hacks knew they were being watched by others in the agency, they would moderate their behavior.