I agree, the budget is really the only tool that Congress has to control them. Only a short-term option, but when the leadership has gotten this corrupt, desperate measures are called for. Stop protecting the law-breakers, cooperate with Congressional Oversight committees, and then as soon as the rot is cleared out and the sunshine is allowed in, they will get their budget restored.
PS I apologize if this seems political, but this is not really about politics, it's about being able to trust the government agency that has been given the most rights to intrude into the privacy of every American of our entire government. The only part of government where you are 'guilty until you prove your innocence' if they say you are, with the power to go into your bank records without getting a court order first, etc.