Incentives work. Figuring out the correct incentives to achieve good results is hard. Keeping ahead of the people who will game them is hard. This requires competent management, which is obviously lacking. Fire the incompetent managers and fire the political leadership who appointed them (term limits might help here).

Since there are credible allegations of crime, is there an inspector general? There should be. If not, bring in the fraud squad and investigate the hell out of them. They'll leave.