I may be missing something, but increased enforcement sounds like a great way to solve the corruption problem?
Eg. Public servants make ends meet by fudging timesheets => Enforcement clamps down on practice => Employees bargain for higher pay to make up for difference => Public gets a more transparent accounting of their labor costs
There's no set of laws that can efficiently govern dishonest people. Or in "low trust" environments, if you prefer think of it amorally.
Enforcement just moves around where the corruption is incentivized to happen. Is it at the bottom -- workers stealing extra pay or higher up where the enforcement happens?
Eg. Public servants make ends meet by fudging timesheets => Enforcement clamps down on practice => Employees bargain for higher pay to make up for difference => Public gets a more transparent accounting of their labor costs